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Finite semigroups with commuting idempotents. (English) Zbl 0634.20032
Let S be a finite semigroup in which every two idempotents commute. The main result of this paper is that each such S is the homomorphic image of a subsemigroup of a finite inverse semigroup. A pseudovariety of semigroups is a class of finite semigroups closed under construction of subsemigroups, finite direct products, and homomorphic images. This aper shows that the class of finite semigroups in which every two idempotents commute is a pseudovariety and is the pseudovariety generated by the class of finite inverse semigroups.