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.
@article{bwmeta1.element.doi-10_2478_s11533-010-0066-8,
author = {Suzana Mendes-Gon\c calves and Robert Sullivan},
title = {Semigroups of transformations restricted by an equivalence},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {1120-1131},
zbl = {1210.20061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0066-8}
}
Suzana Mendes-Gonçalves; Robert Sullivan. Semigroups of transformations restricted by an equivalence. Open Mathematics, Tome 8 (2010) pp. 1120-1131. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0066-8/
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