A Study of Graph Closed Subsemigroups of a Full Transformation Semigroup
نویسندگان
چکیده
Let T x be the full transformation semigroup on the set X and let S be a subsemigroup of Tx. We may associate with S a digraph g(5) with X as set of vertices as follows: / —► / e g(<S) iff there exists a 6 S such that a(i) = /. Conversely, for a digraph C having certain properties we may assign a semigroup structure, S(G), to the underlying set of G. We are thus able to establish a "Galois correspondence" between the subsemigroups of Tx and a particular class of digraphs on X. In general, 5 is a proper subsemigroup of S • 9 (S).
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