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Finite semilattices whose non-invertible endomorphisms are products of idempotents

  • M. E. Adams (a1), Sydney Bulman-Fleming (a2), Matthew Gould (a3) and Amy Wildsmith (a4)

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.

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