The six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based

Abstract

We show that the six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based. More precisely, for every positive integer $n$, we construct an infinite additively idempotent semiring, generated by at most $(6n+8{)}^2$ elements, that satisfies every $n$-variable identity of $B_2^1$.