The structure of certain F-inverse semigroups

Abstract

An inverse semigroup is an F-inverse semigroup if each class modulo the minimum group congruence has a maximum element. This paper studies a class of F-inverse semi-groups in which all these maximum elements form a subgroup. After obtaining some characterizations of such semigroup, the structure theorem is obtained by the semidirect product of a semilattice and a group.

Keywords:

• Inverse semigroup
• Minimum group congruence
• Naturally ordered
• Semidirect product