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Green's Relations for Regular Elements of Semigroups of Endomorphisms

Published online by Cambridge University Press:  20 November 2018

K. D. Magill Jr.  and
S. Subbiah
K. D. Magill Jr.
Affiliation:
State University of New York at Buffalo, Amherst, New York
S. Subbiah
Affiliation:
State University of New York at Buffalo, Amherst, New York
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X is a set and End X is a semigroup, under composition, of functions, which map X into X. We characterize those elements of End X which are regular and then we completely determine Green's relations for these elements. The conditions we place on End X are sufficiently mild to permit such semigroups as S(X), the semigroup of all continuous self maps of a topological space X and L(V), the semigroup of all linear transformations on a vector space V, to be regarded as special cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1484 - 1497
Copyright
Copyright © Canadian Mathematical Society 1974

References

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