On Uσ-Abundant Semigroups
Xueming Ren, Qingyan Yin, K. P. Shum · Algebra Colloquium · 2012
A U-abundant semigroup whose subset U satisfies a permutation identity is said to be Uσ-abundant. In this paper, we consider the minimum Ehresmann congruence δ on a Uσ-abundant semigroup and explore the relationship between the category of Uσ-abundant semigroups (S,U) and the category of Ehresmann semigroups (S,U)/δ. We also establish a structure theorem of Uσ-abundant semigroups by using the concept of quasi-spined product of semigroups. This generalizes a result of Yamada for regular semigroups in 1967 and a result of Guo for abundant semigroups in 1997.