## Papers in preparation

- (with V. Kala and T. Kepka)
*Congruence-simple matrix semirings.*(submitted). - (with J. Paseka and T. Vetterlein)
*Transitivity and divisibility of the symmetry group of orthosets.*(in preparation). - (with T. Kepka)
*The lowest-degree polynomials with non-negative coefficients.*(in preparation).

## Papers in journals

- (with T. Kepka)
*Additively idempotent matrix semirings.*to appear in J. Algebra Appl. - (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**22**(2023), (14pp), doi: 10.1007/s00012-023-00807-7. - (with T. Kepka and G. Landsmann)
*Congruence-simple semirings without nilpotent elements.*J. Algebra Appl.**84**(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. *Homomorphic images of subdirectly irreducible rings.*Comm. Algebra**47(11)**(2019), 4432-4440.- (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

- 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