A study of graph closed subsemigroups of a full transformation semigroup
Authors:
R. G. Biggs, S. A. Rankin and C. M. Reis
Journal:
Trans. Amer. Math. Soc. 219 (1976), 211-223
MSC:
Primary 20M20; Secondary 05C20
DOI:
https://doi.org/10.1090/S0002-9947-1976-0404502-4
MathSciNet review:
0404502
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the full transformation semigroup on the set X and let S be a subsemigroup of
. We may associate with S a digraph
with X as set of vertices as follows:
iff there exists
such that
. Conversely, for a digraph G having certain properties we may assign a semigroup structure,
, to the underlying set of G. We are thus able to establish a ``Galois correspondence'' between the subsemigroups of
and a particular class of digraphs on X. In general, S is a proper subsemigroup of
.
- [1] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961. MR 24 #A2627. MR 0132791 (24:A2627)
- [2] M. Petrich, The translational hull in semigroups and rings, Semigroup Forum 1 (1970), no. 4, 283-360. MR 42 #1919. MR 0267017 (42:1919)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0404502-4
Keywords:
Transformation semigroup,
nil semigroup,
idealizer,
partially ordered set,
digraph,
algebraic graph,
idealized graph
Article copyright:
© Copyright 1976
American Mathematical Society