Semigroups of transformations restricted by an equivalence

Suppose σ is an equivalence on a set X and let E ( X, σ ) denote the semigroup (under composition) of all α : X → X such that σ ⊆ α ∘ α −1 . Here we characterise Green’s relations and ideals in E ( X, σ ). This is analogous to recent work by Sullivan on K ( V, W ), the semigroup (under composition)...

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Published in:Central European journal of mathematics 2010-12, Vol.8 (6), p.1120-1131
Main Authors: Mendes-Gonçalves, Suzana, Sullivan, Robert P.
Format: Article
Language:English
Subjects:
20M20
Algebra
Composition
Equivalence
Geometry
Green’s relations
Ideals
Lie Groups
Linear transformations
Mathematics
Mathematics and Statistics
Number Theory
Probability Theory and Stochastic Processes
Research Article
Semigroups
Topological Groups
Transformation semigroup
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description Suppose σ is an equivalence on a set X and let E ( X, σ ) denote the semigroup (under composition) of all α : X → X such that σ ⊆ α ∘ α −1 . Here we characterise Green’s relations and ideals in E ( X, σ ). This is analogous to recent work by Sullivan on K ( V, W ), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β , where W is a fixed subspace of V .
doi_str_mv 10.2478/s11533-010-0066-8
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identifier ISSN: 1895-1074
ispartof Central European journal of mathematics, 2010-12, Vol.8 (6), p.1120-1131
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2391-5455
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source Publicly Available Content Database; De Gruyter Journals - Open Access
subjects 20M20
Algebra
Composition
Equivalence
Geometry
Green’s relations
Ideals
Lie Groups
Linear transformations
Mathematics
Mathematics and Statistics
Number Theory
Probability Theory and Stochastic Processes
Research Article
Semigroups
Topological Groups
Transformation semigroup
title Semigroups of transformations restricted by an equivalence
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