Characterization of the semilattice of idempotents of a finite-rank permutable inverse semigroup with zero

Abstract

We give a characterization of the semilattice of idempotents of a finite-rank permutable inverse semigroup with zero.

Structure of a finite inverse semigroup with zero every stable order on which is fundamental or antifundamental

“…The structure of the semilattice of idempotents of a permutable inverse semigroup of finite length with zero is clarified in [14]. By using this result, one can readily show that each nonzero idempotent of the semigroup S is a union of atoms in the semilattice E ( S ).…”