Abstract
Green’s relations were first studied by Green in 1951. These relations have played a fundamental role in the development of semigroup theory. Green’s relations are especially significant in the study of regular semigroups. Let V be a vector space over a field F and L(V) the linear transformation semigroup on V. It is well-known that L(V) is regular. To generalize this semigroups, let V and W be vector spaces over a field F and L(V,W) be the set of all linear transformations from V to W. For θ ∈ L(W, V), let (L(V,W), θ) be a semigroup (L(V,W), *) where α * β = αθβ for all α, β ∈ L(V,W). Our purpose in this paper is to characterize regular elements and to characterize L-classes, R-classes, H-classes and D-classes of the semigroup (L(V,W),θ).
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Submitted by M.M. Arslanov
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Chinram, R. Green’s relations and regularity of generalized semigroups of linear transformations. Lobachevskii J Math 30, 253–256 (2009). https://doi.org/10.1134/S1995080209040015
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DOI: https://doi.org/10.1134/S1995080209040015