UNCE / SCI / 022

Methods of Algebra and Logic

Papers

The list below contains papers with one or more authors partially supported by the project (jr-members or students). The online info in each item (usually ArXiv or DOI) points to a web page where is (or eventually will be) a complete biblio info.
Published in 2018, 2019, 2020, 2021, 2022, 2023.

Preprints

  • Chris Lambie-Hanson and Davd Uhrik,
    Hajnal-Mate graphs, Cohen reals, and disjoint type guessing,
    ArXiV: https://browse.arxiv.org/abs/2312.01828

  • O.Celikbas, S.Dey, T.Kobayashi and H.Matsui,
    On reducing projective dimension over local rings,
    preprint 2023,
    DOI: https://doi.org/10.1017/S0017089523000368

  • Michael Kompatscher,
    The subpower membership problem of 2-nilpotent algebras,
    ArXiv: 2309.16549, preprint 2023.

  • O.Celikbas, S.Dey, T.Kobayashi, H.Matsui and A.Sadeghi,
    Two theorems on the vanishing of Ext
    DOI: https://doi.org/10.48550/arXiv.2308.08999

  • Isaac Bird and Jordan Williamson,
    Definable functors between triangulated categories with applications to tensor-triangular geometry and representation theory,
    DOI: https://doi.org/10.48550/arXiv.2310.02159

  • Souvik Dey,
    Strong generation and (co)ghost index for module categories,
    DOI: https://doi.org/10.48550/arXiv.2307.13675

  • D. Gil-Munoz, M. Tinkova,
    The lifting problem for universal quadratic forms over simplest cubic fields,
    Bull. Aust. Math. Soc. (to appear)

  • M. Melistas,
    Torsion and twists of abelian varieties

    D. Gil-Munoz,
    A generalization of Kummer theory to Hopf-Galois extensions
    ArXiv: https://arxiv.org/abs/2305.08648

  • V. Kala, M. Zindulka,
    Partitions into powers of an algebraic number
    ArXiv: http://arxiv.org/abs/2305.16688

  • H. Rada, S. Starosta, V. Kala,
    Periodicity of general multidimensional continued fractions using repetend matrix form
    ArXiv: https://arxiv.org/abs/2307.00898

  • B. Zmija,
    Large gaps between values of several quadratic forms

  • J. Marchwicki, B. Zmija,
    Bounded ranges of cardinal functions

  • N. Daans, V. Kala, S. H. Man,
    Universal quadratic forms and Northcott property of infinite number fields
    ArXiv: https://arxiv.org/abs/2308.16721

  • Michael Kompatscher,
    CSAT and CEQV for nilpotent algebras of Fitting length > 2, submitted
    ArXiv: https://arxiv.org/abs/2105.00689

  • K. J. Becher, N. Daans, D. Grimm, G. Manzano-Flores, M. Zaninelli,
    The Pythagoras number of a rational function field in two variables.
    ArXiv: https://arxiv.org/abs/2302.11425

  • V. Kala, P. Yatsyna, B. Zmija,
    Real quadratic fields with a universal form of given rank have density zero.
    ArXiv: https://arxiv.org/abs/2302.12080

  • T. Crespo, D. Gil-Munoz, A. Rio, M. Vela,
    Double semidirect products and skew left braces of size np.
    ArXiv: https://arxiv.org/abs/2302.13098

  • V. Kala, E. Sgallova, M. Tinkova,
    Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables.
    ArXiv: https://arxiv.org/abs/2303.00485

    V. Kala, T. Kepka, M. Korbelar,
    Congruence-simple matrix semirings.
    ArXiv: http://arxiv.org/abs/2303.06921

  • I. Araujo, B. Frederickson, R. A. Krueger, B. Lidicky, T. B. McAllister, F. Pfender, S. Spiro, E. N. Stucky,
    Triangle Percolation on the Grid.
    ArXiv: https://arxiv.org/abs/2303.15402 

  • Isaac Bird and Jordan Williamson,
    The homological spectrum via definable subcategories
    DOI: https://doi.org/10.48550/arXiv.2304.05179

  • D.Uhrik,
    Complete Bipartite Partition Relations in Cohen Extensions,
    ArXiv: https://arxiv.org/abs/2302.05634

  • G. Cherubini, P. Mercuri,
    Parity of 4-regular and 8-regular partition functions
    Ramanujan J., to app.,
    ArXiv: https://arxiv.org/abs/2212.11356

  • G. Cherubini, P. Yatsyna,
    Degrees of Salem numbers of trace −3,
    ArXiv: https://arxiv.org/abs/2301.06536

  • D. Gil-Munoz, M. Tinkova,
    Additive structure of non-monogenic simplest cubic fields.
    ArXiv: https://arxiv.org/abs/2212.00364 (preprint)

  • V. Kala,
    On continued fraction coefficients of square roots of primes.
    ArXiv: https://arxiv.org/abs/2212.07198 (preprint)

  • B. Zmija, High order congruences for M-ary partitions.

  • Z. Patakova: Bounding Radon number via Betti numbers https://arxiv.org/pdf/1908.01677.pdf

  • David Uhrik,
    The Uncountable Hadwiger Conjecture and Characterizations of Trees Using Graphs,
    ArXiv: https://arxiv.org/abs/2212.02169

  • T.Kania, D.H.Leung and M.Rmoutil,
    Erratum and addendum to "Recovering a compact Hausdorff space X from the compatibility ordering on C(X)",
    Fund. Math. 242 (2018), 187-205.
    DOI: 10.4064/fm170-2-2022

  • B.Hudcova, T.Mikolov,
    Classification of Discrete Dynamical Systems Based on Transients
    doi: 10.1162/artl_a_00342

  • B.Hudcova, T.Mikolov,
    Computational Hierarchy of Elementary Cellular Automata doi: 10.1162/isal_a_00447

  • Liran Shaul,
    Sequence-regular commutative DG-rings,
    ArXiv.



  • X.Goaoc, A.Holmsen, Z.Patakova,
    A Stepping-Up Lemma for Topological Set Systems
    ArXiv/pdf.

  • J. Dudak and B. Vejnar,
    The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension
    ArXiv

  • L.Shaul and J.Williamson,
    Lifting (co)stratifications between tensor triangulated categories,
    Israel Journal of Mathematics, accepted.
    ArXiv

  • A.Slavik, J.Stovicek,
    On flat generators and Matlis duality for quasicoherent sheaves,
    Bulletin of the London Mathematical Society, DOI

  • M.Hrbek, L.Positselski, A.Slavik,
    Countably generated flat modules are quite flat,
    to appear in the Journal of Commutative Algebra,
    Project Euclid.

  • M.Prest, A.Slavik,
    Purity in categories of sheaves,
    Mathematische Zeitschrift,
    DOI.

  • P.Kawalek, M.Kompatscher, and J.Krzaczkowski,
    Circuit equivalence in 2-nilpotent algebras.
    ArXiv

  • A.Slavik,
    Purity in categories of sheaves,
    ArXiv

  • A.Slavik,
    On flat generators and Matlis duality for quasicoherent sheaves
    ArXiv

  • A.Slavik,
    Countably generated flat modules are quite flat,
    ArXiv

  • A.Vernerova and J.Verner,
    PyVallex: a processing system for valnce lexicon data,
    preprint 2019.

  • J.Saroch,
    On the nontrivial solvability of systems of homogeneous linear equations over Z in ZFC,
    Comm.Math.Univ.Carolinae, accepted.
    ArXiv.

  • T.Lavicka and J. Verner,
    Completely separably MAD families and the modal logic of $\beta\omega$,
    J. of Symbolic Logic, to appear.
    ArXiv.

  • Jan Hubicka, Michael Kompatscher and Matej Konecny,
    Forbidden cycles in metrically homogeneous graphs,
    European J. of Combinatorics, to app.,
    ArXiv.

  • G. Cherubini, A. Fazzari,
    Hyperbolic angles from Heegner points.
    Michigan Math J., to app.
    ArXiv: https://arxiv.org/abs/2206.08282

  • V. Kala, L. Sima,
    On generators of commutative semifields,
    ArXiv: https://arxiv.org/abs/2307.07287

  • P. Miska, J. Toth, B. Zmija,
    On distribution of subsequences of primes having prime indices with respect to the (R)-densness and convergence exponent.
    ArXiv: https://arxiv.org/abs/1908.10421.pdf

  • S.Opper,
    Spherical objects, transitivity and auto-equivalences of Kodaira cycles via gentle algebras,
    J.EMS, to app.
    ArXiv: https://arxiv.org/pdf/2011.08288

    Published in 2023

  • B. Zmija, Arithmetic properties of colored p-ary partitions,
    Acta Math. Hungar., 171 (1) (2023), 53-66

  • V. Kala,
    Universal quadratic forms and indecomposables in number fields: A survey.
    Commun.Math, 31(2), (2023), pp.81-114
    DOI: https://doi.org/10.46298/cm.10896

  • J. Glivicka, E. Sgallova, J. Saroch,
    Controlling distribution of prime sequences in discretely ordered principal ideal subrings of Q[x],
    Proc. Amer. Math. Soc., 151, (2023), pp.3281-3290..
    DOI: https://doi.org/10.1090/proc/16358

  • V. Kala, P. Miska, On continued fraction coefficients of square roots of primes.
    \J/Number Th., 253, (2023), pp.215-234.
    DOI: https://dx.doi.org/10.1016/j.int.2023.06.013

  • V. Kala, M. Tinkova,
    Universal quadratic forms, small norms and traces in families of number fields,
    Int. Math. Res. Not. IMRN, 9, (2023), pp.7541-7577.
    DOI: https://doi.org/10.1093/imrn/rnac073

  • G. Cherubini, A. Fazzari, A. Granville, V. Kala, P. Yatsyna,
    Consecutive real quadratic fields with large class numbers,
    Int. Math. Res. Not. IMRN (2023), pp.12052-12063..
    DOI: https://doi.org/10.1093/imrn/rnac176

  • F.Genovese,
    T-structures on unbounded twisted complexes,
    Mathematische Zeitschrift, 305, Articl eno.18 (2023).
    DOI: https://doi.org/10.1007/s00209-023-03340-4

  • M. Tinkova,
    On the Pythagoras number of the simplest cubic fields,
    Acta Arith. 208, (2023) 325-354.
    DOI: https://doi.org/10.4064/aa221003-27-6

  • Jakub Bulin, Michael Kompatscher,
    Short definitions in constraint languages.
    Proceedings of the 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), p28:1--28:15.
    DOI: https://doi.org/10.4230/LIPIcs.MFCS.2023.28

  • M.Tinkova,
    Trace and norm of indecomposable integers in cubic orders,
    Ramanujan J. 61, (2023) 1121-1144.
    DOI: https://doi.org/10.1007/s11139-022-00669-y

  • G. Cherubini, P. Yatsyna,
    Cyclic polytope of the simplest cubic fields,
    Discrete Comput. Geom. 69 (2023), 338-348.
    DOI: https://doi.org/10.1007/s00454-021-00369-2
    ArXiv: https://arxiv.org/abs/2011.04326

  • V. Kala,
    Number fields without universal quadratic forms of small rank exist in most degrees,
    Math. Proc. Cambridge Philos. Soc. 174 (2023), 225-231.
    DOI: https://www.doi.org/10.1017/S0305004122000214
    ArXiv: https://arxiv.org/abs/2101.10364

  • J. Krasenska, P. Yatsyna,
    On quadratic Waring's problem in totally real number fields,
    Proc. Amer. Math. Soc. 151 (2023), 1471-1485.
    DOI: https://doi.org/10.1090/proc/16233
    ArXiv: https://arxiv.org/abs/2112.15243

  • T. Crespo, D. Gil-Munoz, A. Rio, M. Vela,
    Inducing braces and Hopf Galois structures,
    J. Pure Appl. Algebra 227 (9) (2023), 107371.
    DOI: https://doi.org/10.1016/j.jpaa.2023.107371
    ArXiv: https://arxiv.org/abs/2206.03810

  • V. Kala, P. Yatsyna,
    On Kitaoka's conjecture and lifting problem for universal quadratic forms,
    Bull. Lond. Math. Soc. 55 (2), 854-864.
    DOI: http://doi.org/10.1112/blms.12762
    ArXiv: https://arxiv.org/abs/2110.06260

  • D. Gil-Munoz,
    The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure,
    J.of Number Theory, 245 (2023), 65-118.
    DOI: https://doi.org/10.1016/j.jnt.2022.10.002
    ArXiv: https://arxiv.org/abs/2205.13517

  • M. Tinkova, E. Waxman and M. Zindulka,
    Artin twin primes, J. Number Theory 245, (2023) 203-232.
    DOI: 10.1016/j.jnt.2022.10.006
    ArXiv: https://arxiv.org/abs/2010.15988

  • T.Crespo, D.Gil-Munoz, A.Rio, M.Vela,
    Left braces of size 8p, J.of Algebra, 617 (2023), 317-339.
    DOI: https://doi.org/10.1016/j.jalgebra.2022.11.011
    ArXiv: https://arxiv.org/abs/2205.04201

    Published in 2022

  • Pierre Gillibert, Julius Jonuas, M.Kompatscher, Antoine Mottet, Michael Pinsker,
    When symmetries are not enough: A hierarchy of hard constraint satisfaction problems.
    SIAM Journal on Computing, 5(2), 175-213, 2022.
    DOI: https://doi.org/10.1137/20M1383471

  • M.Kompatscher,
    CC-circuits and the expressive power of nilpotent algebras.
    Logical Methods in Computer Science, 18(2), 12:1-12:15, 2022.
    DOI: https://doi.org/10.46298/lmcs-18(2:12)2022

  • Z. Patakova, M. Sharir:
    Covering Points by Hyperplanes and Related Problems
    Proceedings of SoCG 2022: 57, 1--7
    DOI: https://doi.org/10.4230/LIPIcs.SoCG.2022.57

  • Z. Patakova, M. Tancer, U. Wagner:
    Barycentric Cuts Through a Convex Body
    Discrete & Computational Geometry volume??68,??pages 1133???1154 (2022)
    DOI: https://doi.org/10.1007/s00454-021-00364-7

  • Bruin, B.Vejnar:
    Classification of one dimensional dynamical systems by countable structures
    Journal of symbolic Logic, published online
    DOI: https://doi.org/10.1017/jsl.2022.67

  • J. Krasensky, M. Raska, E. Sgallova,
    Pythagoras numbers of orders in biquadratic fields,
    Expo. Math. 40, 1181???1228 (2022).
    DOI: 10.1016/j.exmath.2022.06.002

  • G. Cherubini, P. Yatsyna,
    Potential energy of totally positive algebraic integers,
    J. Math. Anal. Appl. 516 (2) (2022), 126518.
    DOI:??https://doi.org/10.1016/j.jmaa.2022.126518
    ArXiv:??https://arxiv.org/abs/2202.05235

  • G. Cherubini, P. Yatsyna,
    Cyclic polytope of the simplest cubic fields, Discrete Comput Geom (to app).
    DOI:??https://doi.org/10.1007/s00454-021-00369-2
    ArXiv:??https://arxiv.org/abs/2011.04326

  • Tomas Hejda, Vitezslav Kala,
    Ternary quadratic forms representing a given arithmetic progression,
    J. Number Theory??234 (2022), 140???152.
    DOI: https://doi.org/10.1016/j.jnt.2021.09.017
    ArXiv:??https://arxiv.org/abs/1906.02538

  • Alexandr Kazda, Peter Mayr, Dmitriy Zhuk,
    Small Promise CSPs that reduce to large CSPs,
    Logical Methods in Computer Science, August 22, 2022, Volume 18, Issue 3
    DOI, ArXiv

  • Alexandr Kazda, Michael Kompatscher,
    Local-global property for G-invariant terms,
    International Journal of Algebra and Computation. Vol. 32, No. 06, pp. 1209-1231 (2022)
    DOI, ArXiv.

  • S.Opper and A.Zvonareva,
    Derived equivalence classification of Brauer graph algebras
    Advances in Mathematics, Vol.402, (June 2022), 108341.
    DOI and ArXiv.

  • D.Gil-Munoz, A.Rio,
    Hopf Galois module structure of quartic Galois extensions of Q, J. Pure Appl. Algebra 226 (9) (2022), 107045
    DOI: https://doi.org/10.1016/j.jpaa.2022.107045
    ArXiv: https://arxiv.org/abs/2107.13515

  • L.Shaul,
    Open loci results for commutative DG-rings,
    Journal of Pure and Applied Algebra, Volume 226, Issue 5, May 2022, No.106922.
    ArXiv.

  • J. Krasensky,
    A cubic ring of integers with the smallest Pythagoras number,
    Arch. Math. (Basel) 118, 39-48 (2022).
    DOI, also available at arXiv:2107.11772.

  • E.Pelantova, T.Vavra,
    On positional representations of integer vectors,
    Linear Algebra Appl. 633 (2022), 316-331.
    ArXiv: https://arxiv.org/abs/2103.02599,
    DOI: https://doi.org/10.1016/j.laa.2021.10.018.

  • Z.Masakova, T.Vavra, F.Veneziano, Finiteness and periodicity of continued fractions over quadratic number fields, Bull. Soc. Math. Fr. 150 (1) (2022), 77???109. ArXiv: https://arxiv.org/abs/1911.07670

    Published in 2021

  • X. Goaoc, A. Holmsen, Z. Patakova: Stepping-up Lemma for Topological Set Systems Proceedings of SoCG 2021: 40, 1--17 DOI: https://doi.org/10.4230/LIPIcs.SoCG.2021.40 https://arxiv.org/abs/2103.09286

  • B. Vejnar:
    There is no compact metrizable space containing all continua as unique components,
    Topology and its Applications, Volume 299, 1 August 2021, 107742
    DOI: doi.org/10.1016/j.topol.2021.107742

  • B. Faye, L. Matthiesen, D. Schindler, M. Tinkova and K. Zemkova,
    Integers Represented by Ternary Quadratic Forms,
    Women in Numbers Europe III: Research Directions in Number Theory,
    Association for Women in Mathematics Series, vol 24, Springer, (2021) 207-231.
    DOI: https://doi.org/10.1007/978-3-030-77700-5_7

  • T. Vavra,
    Periodic representations in Salem bases.
    Isr. J. Math. 242 (2021), 83-95.
    DOI,
    ArXiv.

  • Libor Barto, Jakub Bulin, Andrei Krokhin, Jakub Oprsal,
    Algebraic approach to promise constraint satisfaction,
    ArXiv
    Journal of the ACM 68/4 (2021), 1-66

  • Vitezslav Kala, Pavlo Yatsyna,
    Lifting problem for universal quadratic forms,
    Adv. Math. 377 (2021), 107497
    DOI, ArXiv.

  • Magdalena Tinkova,
    Arithmetics in number systems with cubic base
    Publ. Math. Debrecen 99, (2021) 25-50.
    DOI,
    ArXiv,

  • Alexandr Kazda, Dmitriy Zhuk,
    Existence of cube terms in finite finitely generated clones",
    Algebra Univers. 82, 11 (2021).
    DOI and ArXiv.

  • Liran Shaul,
    Koszul complexes over Cohen-Macaulay rings,
    Advances in Mathematics, Volume 386, 2021, 107806
    DOI
    ArXiv.

  • Liran Shaul,
    Smooth flat maps over commutative DG-rings,
    Mathematische Zeitschrift, (2021) Volume 299, pp. 1673 - 1688.
    ArXiv, DOI.

  • Alexandr Kazda,
    Deciding the existence of quasi weak near unanimity terms in finite algebras,
    Journal of Multiple-Valued Logic and Soft Computing,36(4-5) (2021) 337-352.
    URL: https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-36-number-4-5-2021/mvlsc-36-4-5-p-337-352/
    ArXiv.

  • L.Shaul and V.Vinnikov,
    Pole placement for overdetermined 2D systems,
    Linear Algebra and its Applications Volume 610, 1 February 2021, Pages 529-559.
    DOI and ArXiv.

    Published in 2020

  • P. Krupski and B. Vejnar,
    The complexity of homeomorphism relations on some classes of compacta,
    Journal of Symbolic Logic 85 (2020) 733-748.
    ArXiv.
    DOI.

  • L.Shaul,
    The Cohen-Macaulay property in derived commutative algebra,
    Transactions of the American Mathematical Society, 373 (2020), no. 9, 6095 - 6138
    DOI, ArXiv.

  • Tomas Hejda, Vitezslav Kala,
    Additive structure of totally positive quadratic integers,
    Manuscripta Math. 163 (2020), 263 - 278.
    DOI: 10.1007/s00229-019-01143-8
    ArXiv.

  • Alexandr Kazda, Matt Valeriote.
    Deciding some Maltsev conditions in finite idempotent algebras,
    J.Symbolic Logic, 85 (2), 2020.
    DOI: 10.1017/jsl.2019.73.
    URL: https://doi.org/10.1017/jsl.2019.73
    ArXiv,

  • Alexandr Kazda, Jakub Oprsal, Matt Valeriote, Dmitriy Zhuk.
    Deciding the existence of minority terms,
    Canadian Mathematical Bulletin, 63(3):577-591, (2020).
    ArXiv
    DOI

  • V. Kala, P. Yatsyna,
    Sums of squares in S-integers,
    New York J. Math. 26 (2020), 1145 - 1154 ( journal url),
    ArXiv.

  • P.Gillibert, J.Jonusas, M.Kompatscher, A.Mottet, M.Pinsker,
    Hrushovski's Encoding and omega-Categorical CSP Monsters,
    47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
    DOI: 10.4230/LIPIcs.ICALP.2020.131

  • J. Krasensky, M. Tinkova, K. Zemkova,
    There are no universal ternary quadratic forms over biquadratic fields,
    Proc. Edinburgh Math. Soc. 63(3), 861???912 (2020).
    doi:10.1017/S001309152000022X

    Published in 2019

  • Jakub Bulin, Andrei Krokhin, Jakub Oprsal,
    Algebraic approach to promise constraint satisfaction,
    Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, June 2019, Pages 602???613.
    DOI: 10.1145/3313276.3316300
    ArXiv.

  • Alexandr Kazda,
    Taylor term does not imply any nontrivial linear one-equality Maltsev condition,
    Algebra Univers. (2019) 80: 9.
    DOI: 10.1007/s00012-019-0580-x
    ArXiv.

  • Michael Kompatscher,
    Some notes on extended equation solvability and identity checking for groups,
    Acta Mathematica Hungarica, 159(1) 246-256, Oct 2019.
    DOI: 10.1007/s10474-019-00924-7
    ArXiv.

  • A. Bartos, J. Bobok, P. Pyrih and B. Vejnar,
    Compactifiable classes of compacta,
    Topology and its Applications 266 (2019), 106836.
    DOI: 10.1016/j.topol.2019.106836
    ArXiv.

  • A. Bartos, J. Bobok, P. Pyrih, S. Roth and B. Vejnar,
    Constant slope, entropy and horseshoes for a map on a tame dendrite,
    Ergodic Theory and Dynamical Systems, 2019, pp.1-25.
    DOI: 10.1017/etds.2019.29
    ArXiv.

  • Magdalena Tinkova and Paul Voutier,
    Indecomposable integers in real quadratic fields,
    J. Number Theory, aa
    DOI: 10.1016/j.jnt.2019.11.005
    ArXiv,

  • Miha E. Habic, and Joel David Hamkins, and Lukas Daniel Klausner, and Jonathan Verner, and Kameryn J. Williams,
    Set-theoretic blockchains,
    Arch. Math. Logic (2019) 58: 965.
    DOI: 10.1007/s00153-019-00672-z

  • Raghavan, Dilip, and Jonathan L. Verner,
    Chains of P-Points,
    Canadian Mathematical Bulletin 62, no. 4 (2019): 856???68.
    DOI: 10.4153/S0008439519000043

    Published in 2018

  • Michael Kompatscher,
    The equation solvability problem over supernilpotent algebras with Malcev term,
    International Journal of Algebra and Computation, (url), 28(6), 1005 - 1015, 2018.
    DOI: 10.1142/S0218196718500443

  • Lovkush Agarwal and Michael Kompatscher
    $2^{\aleph_0}$ pairwise nonisomorphic maximal-closed subgroups of Sym(N) via the classification of the reducts of the Henson digraphs,
    Journal of Symbolic Logic (url), 83(2), 395-415, 2018.
    DOI: 10.1017/jsl.2017.74

  • Vitezslav Kala, Miroslav Korbelar,
    Idempotence of finitely generated commutative semifields,
    Forum Mathematicum, 30(6), 2018. Url,
    DOI: 10.1515/forum-2017-0098.

  • Valentin Blomer, Vitezslav Kala,
    On the Rank of Universal Quadratic Forms over Real Quadratic Fields,
    Doc. Math. 23, 15-34 (2018), Url,
    DOI: 10.25537/dm.2018v23.15-34.

  • Alexander Dahl, Vitezslav Kala,
    Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields,
    Proceedings of the Edinburgh Mathematical Society, 61(4), 2018, 1193-1212. Url,
    DOI: 10.1017/S0013091518000159.