Quasi-ideal Ehresmann transversals: The spined product structure

Abstract

In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼\sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

Keywords

• u-abundant semigroup
• ehresmann transversal
• green’s∼-relations
• quasi-ideal
• spined product
• 20m10