Green's Relations for the Variants of Transformation Semigroups Preserving an Equivalence Relation

Let X be the full transformation semigroup on a set X. For a nontrivial equivalence E on X, let Then T E (X) is a subsemigroup of X . Fix an element θ in T E (X) and define a new operation ○ on T E (X) by f○ g = fθ g where fθ g denotes the product of g, θ, and f in original sense. Under the new oper...

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Bibliographic Details
Published in:Communications in algebra 2007-06, Vol.35 (6), p.1971-1986
Main Authors: Pei, Huisheng, Sun, Lei, Zhai, Hongcun
Format: Article
Language:English
Subjects:
Green's relations
Regular elements
Transformations
Variant semigroups
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Summary:Let X be the full transformation semigroup on a set X. For a nontrivial equivalence E on X, let Then T E (X) is a subsemigroup of X . Fix an element θ in T E (X) and define a new operation ○ on T E (X) by f○ g = fθ g where fθ g denotes the product of g, θ, and f in original sense. Under the new operation, T E (X) forms a semigroup which is called the variant semigroup of T E (X) with the sandwich function θ, and denoted by T E (X; θ). In this article, we characterize the regular elements and describe Green's equivalences for the semigroup T E (X; θ).
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870701247112