Two-element factors and finite bases for additively idempotent semirings

Qirui Ma; Mengya Yue

paper

Two-element factors and finite bases for additively idempotent semirings

arXiv:2610.21605

Abstract

For every additively idempotent semiring $S$ in the constant-free signature, $S$ is finitely based if and only if $S \times E$ is finitely based when $E = M_{2}$ or $T_{2}$ . For each $E \in {L_{2}, R_{2}, D_{2}, N_{2}}$ , both implications fail even for finite $S$ : we give a finite finitely based semiring whose product with $E$ is nonfinitely based and a finite nonfinitely based semiring whose product with $E$ is finitely based.

arXiv comment29 pages