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arXiv · 1701.01282

On completely regular and Clifford ordered semigroups

Anjan Kumar Bhuniya·Kalyan Hansda
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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

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Anjan Kumar Bhuniya, Kalyan Hansda. 2017-01-05. On completely regular and Clifford ordered semigroups. https://arxiv.org/abs/1701.01282

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