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- Title
Weak inverses modulo Green's relation $$\mathcal{{H}}$$ on E-inversive and group-closed semigroups.
- Authors
Fan, Xingkui; Chen, Qianhua; Kong, Xiangjun
- Abstract
In this paper we study semigroups defined either by means of weak inverses modulo Green's relation $$\mathcal{{H}}$$ , or by means of the set of completely regular elements. Basic properties of E-inversive semigroups are analyzed, and semigroups whose completely regular elements form a subsemigroup or a rectangular band modulo $$\mathcal{{H}}$$ are considered. We obtain results that generalize the corresponding results for E-semigroups or semigroups whose idempotents form a rectangular band, and also new results for E-inversive semigroups.
- Subjects
SEMIGROUPS (Algebra); COMPLETELY regular codes; GENERALIZED inverses of linear operators; IDEMPOTENTS; T-matrix
- Publication
Semigroup Forum, 2016, Vol 92, Issue 3, p691
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-015-9773-6