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arXiv · 2303.06921

Congruence-simple matrix semirings

Vítězslav Kala·Tomáš Kepka·Miroslav Korbelář
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Abstract

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 semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a semiring $S$, is congruence-simple, provided that either $S$ has a multiplicatively absorbing element or $S$ is commutative and additively cancellative.

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Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář. 2023-03-13. Congruence-simple matrix semirings. https://doi.org/10.1142/s0218196724500152

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