The finite basis problem for matrix semirings over a two-element additively idempotent semiring

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Jun Jiao, Miaomiao Ren
Cited by: 0

Abstract

We provide a complete classification of matrix semirings $\mathbf{M}_n(S)$ over two-element additively idempotent semirings $S$ with respect to the finite basis property.Our main theorem shows that for every integer $n \geq 2$,the semiring $\mathbf{M}_n(S)$ is finitely based if and only if $S$ is distinct from a distributive lattice.

Fields of Study & Subjects

semigroups and automata theory Advanced Algebra and Logic Rings Modules and Algebras

Publication details

Journal / source
arXiv (Cornell University)
Publication date
12 January 2026
Language
EN
Document type
Preprint