Semiring and involution identities of powers of inverse semigroups

Abstract

The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural conditions on a finite inverse semigroup guaranteeing that neither semiring nor involution identities of the involution semiring of its subsets admit a finite identity basis. © 2023 Taylor & Francis Group, LLC.