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arXiv · 2207.08160

Congruence-simple multiplicatively idempotent semirings

Tomáš Kepka·Miroslav Korbelář·Günter Landsmann
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Abstract

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 either $|S|=2$ or $S\cong End(L)$ or $S^{op}\cong End(L)$ where $L$ is a 2-element semilattice. It seems to be an open question, whether $S$ can be infinite at all.

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Tomáš Kepka, Miroslav Korbelář, Günter Landsmann. 2022-07-17. Congruence-simple multiplicatively idempotent semirings. https://arxiv.org/abs/2207.08160

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