A Structure Preserving Embedding of Semigroups Into Regular Semigroups |
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Authors: | P G Trotter |
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Institution: | 1. School of Mathematics and Physics , University of Tasmania , Hobart , Tasmania , Australia Peter.Trotter@utas.edu.au |
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Abstract: | For any semigroup S a regular semigroup 𝒞(S) that embeds S can be constructed as the direct limit of a sequence of semigroups each of which contains a copy of its predecessor as a subsemigroup whose elements are regular. The construction is modified here to obtain an embedding of S into a regular semigroup R such that the nontrivial maximal subgroups of R are isomorphic to the Schützenberger groups of S and such that the restriction to S of any of Green's relations on R is the corresponding Green's relation on S. |
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Keywords: | Embedding Regular semigroups Semigroups Structure |
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