On Uσ-Abundant Semigroups-Reference-Cited by-同舟云学术

On Uσ-Abundant Semigroups

Published:2012-03 Issue:01 Volume:19 Page:41-52
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Ren Xueming¹,Yin Qingyan¹,Shum K. P.²

Affiliation:

1. Department of Mathematics, Xi'an University of Architecture and Technology, Xi'an 710055, China

2. Institute of Mathematics, Yunnan University, Kunming 650091, China

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S100538671200003X

Reference12 articles.

1. Restriction categories I: categories of partial maps

2. Idempotent-connected abundant semigroups

3. A Munn Type Representation for a Class of E-Semiadequate Semigroups

4. Fundamental Ehresmann semigroups

5. Abundant semigroups whose idempotents satisfy permutation identities

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. LEFT QUASI-ABUNDANT SEMIGROUPS;J KOREAN MATH SOC;2019

2. U-Abundant Semigroups with Ehresmann Transversals;Algebra Colloquium;2018-08-14

3. The structure of -inverse semigroups;Communications in Algebra;2017-11-06

4. Beyond regular semigroups;Semigroup Forum;2015-04-07

5. On U-ample ω-semigroups;Frontiers of Mathematics in China;2013-10-23