The variety of commutative additively and multiplicatively idempotent semirings
The variety of commutative additively and multiplicatively idempotent semirings
The variety $${\mathcal Z}$$ of commutative additively and multiplicatively idempotent semirings is studied. We prove that $${\mathcal Z}$$ is generated by a single subdirectly irreducible three-element semiring and it has a canonical form for its terms. Hence, $${\mathcal Z}$$ is locally finite despite the fact that it is residually large. …