On completely regular and Clifford ordered semigroups
Rings and Algebras
2017-01-06 v1
Abstract
Lee and Kwon [12] defined an ordered semigroup S to be completely regular if a 2 (a2Sa2] for every a 2 S. We characterize every completely regular ordered semigroup as a union of t-simple subsemigroups, and every Clifford ordered semigroup as a complete semilattice of t-simple subsemigroups. Green's Theorem for the completely regular ordered semigroups has been established. In an ordered semigroup S, we call an element e an ordered idempotent if it satisfies e ? e2. Different characterizations of the regular, completely regular and Clifford ordered semigroups are done by their ordered idempotents. Thus a foundation for the completely regular ordered semigroups and Clifford ordered semigroups has been developed
Cite
@article{arxiv.1701.01282,
title = {On completely regular and Clifford ordered semigroups},
author = {Anjan Kumar Bhuniya and Kalyan Hansda},
journal= {arXiv preprint arXiv:1701.01282},
year = {2017}
}
Comments
18 pages, 1 figures