Proper covers for LU-ample type B semigroups

Jiangping Xiao, Yonghua Li

Abstract


A LU-semiadequate semigroup is a semigroup whose projections commute and in which each LU- class contains a projection. Let (S,U) be a LU-semiadequate semigroup, whereU is the set of projections of S. It is the fact that each LU-class of (S,U) contains a unique projection. For an element a of (S,U), the projection in the LU-class containing a is denoted by a∗. Let 1 be an identity of S1, U1=U ∪{1}. If (S,U) satisfying: (1) for all e, f in U1and all elements a in (S,U), (efa)∗= (ea)∗(fa)∗; (2) for all elements a in (S,U) and all projections e ≤ a∗, there is an element f in U1such that e = (fa)∗, then we say that (S,U) is a LU-ample type B semigroup. In this paper, we introduce the concept of a proper cover of a LU-ample type B semigroup and prove that any proper cover for a LU-ample type B semigroup is a proper cover over a monoid. A structure theorem of proper covers for LU-ample type B semigroups is obtained. This theorem generalizes the result of Li-Wang for right type B semigroups.

Full Text: PDF

Published: 2016-03-26

How to Cite this Article:

Jiangping Xiao, Yonghua Li, Proper covers for LU-ample type B semigroups, J. Semigroup Theory Appl., 2016 (2016), Article ID 3

Copyright © 2016 Jiangping Xiao, Yonghua Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

Editorial Office: [email protected]

Copyright ©2024 SCIK Publishing Corporation