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math.RA2024
Torsion factors of commutative monoid semirings
Miroslav Korbelář
Let be a finitely generated commutative semiring. It was shown recently that if is a parasemifield (i.e. the multiplicative reduct of is a group) then cannot contai…
math.RA2023
Congruence-simple matrix semirings
Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář
It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semirin…
math.RA2022
Congruence-simple multiplicatively idempotent semirings
Tomáš Kepka, Miroslav Korbelář, Günter Landsmann
Let be a multiplicatively idempotent congruence-simple semiring. We show that if has a multiplicatively absorbing element. We also prove that if is finite then…