Title: Ockham Congruences Whose Quotient Algebras Are Boolean
Abstract: 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). Key Words: Ockham algebraCongruenceFalsity idealpro-boolean ideal1991 Mathematics Subject Classification: 06D30 Acknowledgment We are grateful to Professor Blyth for helpful discussions on the presentation of the results in this paper.
Publication Year: 2003
Publication Date: 2003-01-10
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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