Some Orthodox Monoids with Associate Inverse Subsemigroups

Abstract

By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x ∈ S, in relation to the natural partial order ≤ _S in S. In this article, we investigate a class of orthodox monoids with an associate inverse subsemigroup and obtain a known description of uniquely unit regular orthodox semigroups as a corollary. Also, by considering a more general situation, we identify the homomorphic image of a kind of semidirect product of a band with identity by an inverse monoid, thus extending a known result for unit regular orthodox semigroups.

Key Words:

• Associate inverse subsemigroup
• Orthodox semigroup
• F-Semigroups

2000 Mathematics Subject Classification:

• Primary 20M10

ACKNOWLEDGMENT

Research supported by the Portuguese Foundation for Science and Technology (FCT) through the Research Centre CMAT.

Notes

Communicated by V. Gould.