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.
Acknowledgments
The authors thank the anonymous referee for careful reading and Edmond W. H. Lee for valuable remarks.
Notes
1 A word of warning appears to be in place here: even though we retain the notation and the name “inversion”, in general, the subset is not the inverse of A in the sense of the above definition of an inverse element!