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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…
math.RA2004
Hamiltonian selfdistributive quasigroups
Dolors Herbera, Tomás Kepka, Petr Nemec
The problem of the existence of non-medial distributive hamiltonian quasigroups is solved. Translating this problem first to commutative Moufang loops with operators, then to terna…