On a Class of Subdirect Products of Left and Right Clifford Semigroups

Abstract

Regular semigroups S with the property eS ⊆ Se or Se ⊆ eS for all idempotents e ∈ S include all left and right Clifford semigroups. Characterizations of such semigroups are given and their structure investigated, in particular in terms of spined products of left and right Clifford semigroups with respect to Clifford semigroups.

Key Words:

• Clifford semigroup
• Left Clifford semigroup
• Left inverse semigroup
• Quasi-inverse semigroup
• Quasi-C-semigroup
• Regular band
• Spined product

2000 AMS Mathematics Subject Classification:

• Primary 20M17

Acknowledgment

The authors gratefully acknowledge the suggestions made by the learned referee which definitely improved the final version of the paper.

Notes

^#Communicated by D. Easdown.