On completely regular and Clifford ordered semigroups
Anjan Kumar Bhuniya, Kalyan Hansda
TL;DR
This paper characterizes completely regular and Clifford ordered semigroups, showing their structure as unions or semilattices of t-simple subsemigroups and establishing Green's Theorem for these structures.
Contribution
It provides new characterizations and structural descriptions of completely regular and Clifford ordered semigroups using ordered idempotents and Green's Theorem.
Findings
Complete characterization of completely regular ordered semigroups.
Representation of Clifford ordered semigroups as semilattices of t-simple subsemigroups.
Establishment of Green's Theorem for these semigroups.
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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