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Properties of a set of idempotent elements of generalised inverse semigroups

Lipińska J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 3

93-97

In the last paper we considered properties of partial order in a generalized inverse semigroup. In this paper we show that a set of idempotent elements of a generalized inverse semigroup is a commutative generalised inverse semigroup. The next problem which appears is if the only commutative inverse semigroups are these which consist of idempotent elements. We prove that it is not the case. We show the commutative inverse semigroup which do not consist only of idempotent elements. We also demonstrate that this inverse generalised semigroup is isomorphic to Ehresmann's pseudogroup.