The set of idempotents of a completely regular semigroup as a binary algebra
TLDR
In this paper, a semigroup S is called E-solid if and only if for all idempotents e, f, g ∈ S such that e L f R g there exists an idemepotent h ∈ s such that R h L g.Abstract:
A semigroup S is called E-solid if and only if for all idempotents e, f, g ∈ S such that e L f R g there exists an idempotent h ∈ S such that e R h L g . Each completely regular semigroup is E-solid. We characterise the idempotents of an arbitrary E-solid regular semigroup as a set with a binary operation on it satisfying a given finite set of identities.read more
Citations
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A concept of variety for regular biordered sets
TL;DR: In this article, the authors define a bivariety of regular biordered sets, which is a nonempty class of sets which is closed under taking direct products, regular bimorphic images and relatively regular subsets, and show that there is a complete lattice morphism mapping all e-varieties of E-solid regular semigroups onto the complete lattices of all varieties of solid binary algebras.
Journal ArticleDOI
Structure theory of regular semigroups
TL;DR: A survey of the structure theory of regular semigroups can be found in this article, where the authors give an overview of several substantial developments of the last 50 years in semigroup structure theory.
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The structure of solid binary algebras
TL;DR: In this paper, the authors present a structure theorem for solid binary algebras in terms of semilattices and rectangular bands, and also show that a free solid binary algebra can be embedded in a free completely regular semigroup.
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E-solid regular semigroups and solid binary algebras
TL;DR: In this paper, the authors derived a similar characterisation of the idempotents of E-solid regular semigroups (which will coincide with the usual band of idempotsents if the semigroup is orthodox) and established a concept of variety for regular biordered sets which is analogous to the concept of existence variety (e-variety).
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Book
Techniques of semigroup theory
TL;DR: In this article, free inverse semigroups and the theorems of McAlister Biordered sets Zigzags and their applications are discussed. But they do not cover the application of ZigZags in word problems.