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Bi-ideals in Clifford ordered semigroup

Kalyan Hansda — 2013

Discussiones Mathematicae - General Algebra and Applications

In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ideals and quasi-ideals. Also we characterize principal bi-ideal generated by an ordered idempotent in a completely regular ordered semigroup.

On the subsemigroup generated by ordered idempotents of a regular semigroup

Anjan Kumar Bhuniya; Kalyan Hansda — 2015

Discussiones Mathematicae - General Algebra and Applications

An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup $g e n e r a t e d b y t h e s e t o f a l l o r d e r e d i d e m p o t e n t s o f a r e g u l a r o r d e r e d s e m i g r o u p S . I f S i s a r e g u l a r o r d e r e d s e m i g r o u p t h e n$ is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.

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