A study of graph closed subsemigroups of a full transformation semigroup

Author:

Biggs R. G.,Rankin S. A.,Reis C. M.

Abstract

Let T X {T_X} be the full transformation semigroup on the set X and let S be a subsemigroup of T X {T_X} . We may associate with S a digraph g ( S ) g(S) with X as set of vertices as follows: i j g ( S ) i \to j \in g(S) iff there exists α S \alpha \in S such that α ( i ) = j \alpha (i) = j . Conversely, for a digraph G having certain properties we may assign a semigroup structure, S ( G ) S(G) , to the underlying set of G. We are thus able to establish a “Galois correspondence” between the subsemigroups of T X {T_X} and a particular class of digraphs on X. In general, S is a proper subsemigroup of S g ( S ) S \cdot g(S) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference2 articles.

1. Mathematical Surveys, No. 7;Clifford, A. H.,1961

2. The translational hull in semigroups and rings;Petrich, Mario;Semigroup Forum,1970

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3. Introduction;Graphs and Order;1985

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