Studia Logica

, Volume 98, Issue 1–2, pp 237–250 | Cite as

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 pK1,1- 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.

Keywords

Ockham algebra pseudocomplementation endomorphism 

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References

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    Blyth T.S., Jie Fang, Varlet J.C.: ‘Ockham algebras with pseudocomplementation’. Communications in Algebra 25, 3605–3615 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of St AndrewsSt AndrewsScotland
  2. 2.School of Computer ScienceGuangdong Polytechnic Normal UniversityGuangdongP.R. China

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