The Finite Basis Problem for Kauffman Monoids

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 $nge 3$. This result holds also for the case when $mathcal{K}_n$ is considered as an involution semigroup under either of its natural involutions.