Ockham congruences whose quotient algebras are boolean

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Abstract

Given any Ockham algebra, we describe the congruences such that the quotient algebras are boolean. This description is obtained using certain ideals that we call pro-boolean ideals. We prove that every proper pro-boolean ideal is the intersection of a family of falsity ideals. We also determine when every proper pro-boolean ideal is a unique intersection of such ideals. Finally, we show that if an Ockham algebra in the Urquhart class P n+2,n is fixed point free then the corresponding dual space has a fixed point. This result is a natural generalisation of a well known theorem (Blyth, T. S., Varlet, J. C. (1994). Ockham Algebras. Oxford University Press, Theorem 6.3).
Original languageEnglish
Pages (from-to)5391-5404
JournalCommunications in Algebra
Volume31
Issue number11
DOIs
Publication statusPublished - 31 Aug 2006

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Keywords

  • Ockham algebra
  • pro-boolean ideal
  • Congruence
  • Falsity ideal

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