, Volume 98, Issue 1-2, pp 237-250

On Endomorphisms of Ockham Algebras with Pseudocomplementation

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Abstract

A pO-algebra \({(L; f, \, ^{\star})}\) is an algebra in which (L; f) is an Ockham algebra, \({(L; \, ^{\star})}\) is a p-algebra, and the unary operations f and \({^{\star}}\) commute. Here we consider the endomorphism monoid of such an algebra. If \({(L; f, \, ^{\star})}\) is a subdirectly irreducible pK 1,1- algebra then every endomorphism \({\vartheta}\) is a monomorphism or \({\vartheta^3 = \vartheta}\) . When L is finite the endomorphism monoid of L is regular, and we determine precisely when it is a Clifford monoid.