The Finite Basis Problem for Kauffman Monoids

Abstract

We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid ${\mathcal{K}}_n$ are nonfinitely based for each $n\ge 3$. This result holds also for the case when ${\mathcal{K}}_n$ is considered as an involution semigroup under either of its natural involutions.

18 pages, 3 figures