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arXiv · 2608.29961

Congruence-simple multiplicatively idempotent semirings and multiplicative divisibility

Damian Siejwa
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Abstract

We resolve two conjectures concerning multiplicatively idempotent semirings. First, we prove that every congruence-simple multiplicatively idempotent semiring is finite, and hence belongs to the finite classification of Kepka, Korbel\'a\v{r} and Landsmann. Second, we prove that every finitely generated commutative multiplicatively divisible semiring is multiplicatively idempotent.

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Damian Siejwa. 2026-08-30. Congruence-simple multiplicatively idempotent semirings and multiplicative divisibility. https://arxiv.org/abs/2608.29961

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