Displaying similar documents to “Generalized Groups with the Well-Ordered Set of Idempotents”

Pointed principally ordered regular semigroups

T.S. Blyth, G.A. Pinto (2016)

Discussiones Mathematicae General Algebra and Applications

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An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = max{y ∈ S | xyx ⩽ x}. Here we investigate those principally ordered regular semigroups that are pointed in the sense that the classes modulo Green's relations ℒ,ℛ,𝒟 have biggest elements which are idempotent. Such a semigroup is necessarily a semiband. In particular we describe the subalgebra of (S;*) generated by a pair of comparable idempotents that are 𝒟-related. We also prove that those...

On the subsemigroup generated by ordered idempotents of a regular semigroup

Anjan Kumar Bhuniya, Kalyan Hansda (2015)

Discussiones Mathematicae - General Algebra and Applications

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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.