The additively idempotent semiring $S_7^0$ is nonfinitely based

TL;DR

This paper proves that the additively idempotent semiring $S_7^0$ cannot be characterized by any finite set of algebraic equations, resolving an open problem in algebraic theory.

Contribution

It demonstrates that the semiring $S_7^0$ is nonfinitely based, providing a significant answer to an open question in the field.

Findings

$S_7^0$ has no finite basis for its equational theory

Resolved an open problem posed by Jackson et al.

Contributes to the understanding of algebraic structures in semiring theory.

Abstract

We show that the additively idempotent semiring $S_7^0$ has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J. Algebra 611 (2022), 211--245).