Miroslav Korbelář

activity

20222024

collaborators

4 papers

math.RA2024

Torsion factors of commutative monoid semirings

Miroslav Korbelář

Let $P$ be a finitely generated commutative semiring. It was shown recently that if $P$ is a parasemifield (i.e. the multiplicative reduct of $P$ is a group) then $P$ cannot contai…

math.RA2023

Additively idempotent matrix semirings

Tomáš Kepka, Miroslav Korbelář

Let $S$ be an additively idempotent semiring and $M_{n} (S)$ be the semiring of all $n \times n$ matrices over $S$ . We characterize the conditions of when the semiring $\mathb…

math.RA2022

Congruence-simple multiplicatively idempotent semirings

Tomáš Kepka, Miroslav Korbelář, Günter Landsmann

Let $S$ be a multiplicatively idempotent congruence-simple semiring. We show that $∣ S ∣ = 2$ if $S$ has a multiplicatively absorbing element. We also prove that if $S$ is finite then…

math.RA2022

Congruence-simple semirings without nilpotent elements

Tomáš Kepka, Miroslav Korbelář, Günter Landsmann

We provide a classification of congruence-simple semirings with a multiplicatively absorbing element and without non-trivial nilpotent elements.