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Finite semilattices whose non-invertible endomorphisms are products of idempotents

Published online by Cambridge University Press:  14 November 2011

M. E. Adams ,
Sydney Bulman-Fleming ,
Matthew Gould  and
Amy Wildsmith
M. E. Adams
Affiliation:
Department of Mathematics, State University of New York, New Paltz, NY 12561, U.S.A.
Sydney Bulman-Fleming
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
Matthew Gould
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A.
Amy Wildsmith
Affiliation:
Department of Mathematics, David Lipscomb University, Nashville, TN 37204, U.S.A.
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Abstract

For a finite semilattice S, is is proved that if every noninvertible endomorphism is a product of idempotents, then S is a chain; the converse was proved, independently, by A. Ya. Aĭzenštat and J. M. Howie. For a finite pseudocomplemented semilattice S, with pseudocomplementation regarded as a unary operation, it is proved that all noninvertible endomorphisms are products of idempotents if and only if S is Boolean or a chain.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1193 - 1198
Copyright
Copyright © Royal Society of Edinburgh 1994

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