On Square-Increasing Ordered Monoids and Idempotent Semirings

Abstrakt

Let V be the variety of square-increasing idempotent semirings. Its members can be viewed as semilattice-ordered monoids satisfying x <= x^2. We show that the universal theory of V is decidable. In order to prove this result, we investigate the class Q whose members are ordered-monoid subreducts of members from V. In particular, we prove that finitely generated members from Q are well-partially-ordered and residually finite.