1. U-Abundant Semigroups with Ehresmann Transversals
- Author
-
Xueming Ren, Siyao Ma, and Chunmei Gong
- Subjects
Pure mathematics ,Class (set theory) ,Algebra and Number Theory ,Mathematics::Operator Algebras ,Applied Mathematics ,010102 general mathematics ,Astrophysics::Solar and Stellar Astrophysics ,Congruence (manifolds) ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Astrophysics::Galaxy Astrophysics ,Mathematics - Abstract
A class of weakly U-abundant semigroups satisfying the congruence condition (C) is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition (C) with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.
- Published
- 2018