(with T. Kepka) The lowest-degree polynomials with non-negative coefficients. (in preparation).
Papers in journals
(with J. Paseka and T. Vetterlein) Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation. J. Geom. 116 , 33 (2025).
(with T. Kepka) Additively idempotent matrix semirings. J. Algebra Appl. 24(1) (2025), 2550013 (20pp).
(with V. Kala and T. Kepka) Congruence-simple matrix semirings. Int. J. Algebr. Comput. 34(3) (2024), 407-424.
(with J. Tolar) Clifford group is not a semidirect product in dimensions N divisible by four. J. Phys. A: Math. Theor. 56 (2023), 275304 (29pp).
Torsion factors of commutative monoid semirings. Semigroup Forum 106 (2023), 662-675.
(with T. Kepka and G. Landsmann) Congruence-simple multiplicatively idempotent semirings. Algebra Universalis 84(13) (2023), (14pp), doi: 10.1007/s00012-023-00807-7.
(with T. Kepka and G. Landsmann) Congruence-simple semirings without nilpotent elements. J. Algebra Appl. 22(9) (2023), 2350195 (11pp), doi: 10.1142/S0219498823501955.
(with T. Kepka and P. Němec) Simple semirings with a bi-absorbing element. Semigroup Forum, 101(2) (2020), 406-420.
(with V. Kala) Idempotence of finitely generated commutative semifields. Forum Math. 30(6) (2018), 1461-1474.
Divisibility and groups in one-generated semirings. J. Algebra Appl. 17(4) (2018), 1850071 (10 pp), doi: 10.1142/S0219498818500718.
(with J. Cibulka, J. Kynčl, V. Meszáros, R. Stolař and P. Valtr) On three measures of non-convexity. Israel J. Math. 218(1) (2017), 331-369.
(with G. Landsmann) One-generated semirings and additive divisibility. J. Algebra Appl. 16(2) (2017), 1750038 (22pp), doi: 10.1142/ S0219498817500384.
Torsion and divisibility in finitely generated commutative semirings. Semigroup Forum 95(2) (2017), 293-302.
(with T. Kepka) Conjectures on additively divisible commutative semirings. Math. Slovaca 66(5) (2016), 1059-1064.
(with J. Tolar) Symmetries of finite Heisenberg groups for multipartite systems. J. Phys. A: Math. Theor. 45(28) (2012), 285305 (18pp).
2-generated nilpotent algebras and Eggert's conjecture. J. of Algebra 324(7) (2010), 1558-1576.
(with V. Kala) Congruence simple subsemirings of Q+. Semigroup Forum 81(2) (2010), 286-296.
(with J. Tolar) Symmetries of the finite Heisenberg group for composite systems. J. Phys. A: Math. Theor. 43(37) (2010), 375302 (15pp).
(with V. Kala and T. Kepka) Notes on commutative parasemifields. Comment. Math. Univ. Carolin. 50(4) (2009), 521-533.
(with T. Kepka) Various examples of parasemifields. Acta Univ. Carol., Math. Phys. 50(1) (2009), 61-72.
(with V. Kala, T. Kepka and J.D. Phillips) Various subsemirings of the field Q of rational numbers. Acta Univ. Carol., Math. Phys. 50(1) (2009), 29-59.
Papers in conference proceedings
(with J. Tolar) Symmetries of finite Heisenberg groups for k-partite systems. In: Č. Burdík, et al (eds.), 7th International Conference on Quantum Theory and Symmetries, J. Phys.: Conf. Ser., 2012, 343, 012122 (6pp).
(with O. Klíma and L. Polák) Rewriting in varieties of idempotent semigroups. In: F. Winkler (ed.). Algebraic informatics: 4-th international conference, CAI 2011. 6742 LNCS, Springer, 2011, 185-200.
Invited talks
August 2012 - Symmetries of finite Heisenberg groups and their applications, The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China
Talks at conferences
July 2024 - Clifford group as a semidirect product, ISQS28, Prague, Czech Republic
November 2022 - Congruence-simple semirings of some classes, Workshop on General Algebra and Ordered Sets, Soláň, Czech Republic
June 2022 - Congruence-simple semirings of some classes, 102th Workshop on General Algebra (AAA102), Szeged,Hungary
September 2021 - On matrix semirings, Workshop on General Algebra and Ordered Sets, Soláň, Czech Republic
July 2021 - Subrings of polynomial rings and divisibility, Conference on Rings and Polynomials, Graz, Austria
June 2021 - Additively regular semirings and divisibility, 101th Workshop on General Algebra (AAA101), Novi Sad, Serbia
September 2019 - Simple semirings with a bi-absorbing element, The 57th Summer School on Algebra and Orded Sets, Karolinka, Czech Republic
March 2019 - Divisible factors of commutative semirings, Arbeitstagung Allgemeine Algebra (AAA 97), Vienna, Austria
August 2018 - On extending properties from integral polynomial rings to their subrings, Workshop & XVIII International Conference on Representations of Algebras, Prague, Czech republic
July 2018 - On Clifford groups and symmetries in quantum computing, The XXXII International Colloquium on Group-Theoretical Methods in Physics, Prague, Czech republic
September 2017 - Homomorphic images of subdirectly irreducible rings, STA '17, Prague, Czech Republic
June 2017 - Homomorphic images of subdirectly irreducible rings, The 94th Workshop on General Algebra (AAA94) & The 5th Novi Sad Algebraic Conference (NSAC2017), Novi Sad, Serbia
May 2016 - Divisibility and torsion in commutative semirings with several generators, The 92nd Workshop on General Algebra (AAA92), Prague, Czech Republic
September 2015 - Divisibility in semigroup rings, The 53rd Summer School on Algebra and Orded Sets, Srní, Czech Republic
February 2015 - Notes on sets of lattice points associated to commutative semirings, The 89th Workshop on General Algebra (AAA89), Dresden, Germany
September 2014 - Idempotency in commutative semirings, The 52nd Summer School on Algebra and Orded Sets, Stará Lesná, Slovakia
June 2014 - Quantum theory and semifields, 12th Biennial IQSA Meeting, Olomouc, Czech Republic
June 2014 - Simple commutative semirings in the context of number theory, ALaNT3, Bedlewo, Poland
February 2014 - Idempotency and finitely generated semifields, The 87th Workshop on General Algebra (AAA87) & The 28th Conference of Young Algebraists (CYA28), Linz, Austria
September 2013 - Additive divisibility and torsion in commutative semirings: The 1-generated case, The 51st Summer School on Algebra and Orded Sets, Trojanovice, Czech Republic
July 2011 - Commutative semirings: simple and additively divisible, Groups and Semigroups: Interactions and Computations, Lisboa, Portugal
July 2011 - Invisibility graphs and free metabelian groups (poster), Linear Groups and Group Representations: Classification Problems, Milan, Italy
August 2010 - Symmetries and fine gradings of sl(n, C), XIV International Conference on Representations of Algebras, Tokyo, Japan
June 2010 - Additively divisible commutative semirings, International Conference on Algebras and Lattices, Prague, Czech Republic
June 2010 - Congruence-simple subsemirings of Q+, The 80th Workshop on General Algebra (AAA80), Bedlewo, Poland
August 2009 - 2-generated nilpotent algebras and Eggert's conjecture, Workshop on Algebra, Combinatorics and Dynamics, Belfast, UK
August 2009 - Symmetries and fine gradings of sl(n, C) generated by tensor products of generalized Pauli matrices (poster), XVI International Congress on Mathematical Physics, Prague, Czech Republic
April 2009 - 2-generated nilpotent algebras and Eggert's conjecture, Joint Meeting of the 61st British Mathematical Colloquium & The 22nd Annual Meeting of the Irish Mathematical Society, Galway, Ireland
September 2008 - Subdirectly irreducible commutative radical rings (poster), Interactions between representation theory and commutative algebra, Barcelona, Spain
July 2008 - Maximal subsemirings of the semiring of positive rational numbers Q+, The 46th Summer School on Algebra and Ordered Sets, Třešť, Czech Republic
Talks at local workshops and seminars
September 2020 - Commutative semirings and divisibility, Workshop on Algebra and Orded Sets, Karolinka, Czech Republic
August 2020 - On simple semirings and related problems, Computer algebra seminar, RISC Johannes Kepler University, Hagenberg, Austria
April 2017 - Homomorphic images of subdirectly irreducible rings, Algebraic seminar FMP CU, Prague, Czech Republic
October 2016 - Finitely generated modules over commutative semirings, ECI Workshop, Třešť, Czech Republic
December 2015 - Symmetries in finite-dimensional quantum mechanics, seminar FEE CTU, Prague, Czech Republic
October 2015 - Divisibility and torsion in semigroup rings, ECI Workshop, Třešť, Czech Republic
October 2014 - Open problems in commutative semirings, seminar FEE CTU, Prague, Czech Republic
April 2014 - Idempotency and 3-generated semifields, AMeGA and ECI Workshop, Třešť, Czech Republic
October 2013 - Additive divisibility and torsion in commutative semirings, AMeGA and ECI Workshop, Třešť, Czech Republic
June 2013 - Computational aspects of recent problems in commutative semirings, Computer algebra seminar, RISC Johannes Kepler University, Hagenberg, Austria
April 2011 - Symmetries, fine gradings of sl(n, C) and mutually unbiased bases, Computer algebra seminar, RISC Johannes Kepler University, Hagenberg, Austria
September 2010 - Symmetries and fine gradings of sl(n, C), ECC Workshop on Categories, Algebras and Representations, Prague, Czech Republic
January 2010 - Eggert’s conjecture and standard bases, Computer algebra seminar, RISC Johannes Kepler University, Hagenberg, Austria
Participations on courses on computer algebra and/or representation theory
January 2010 - Advanced School and Conference on Homological and Geometrical Methods in Representation Theory, International Centre for Theoretical Physics, Trieste, Italy
July 2009 - The 4th RISC/SCIEnce Training School in Symbolic Computation, Hagenberg, Austria
June 2009 - International School on Computer Algebra, Barcelona, Spain