Contributions to the theory of Ockham algebras
MetadataShow full item record
Altmetrics Handle Statistics
In the first part of this thesis we consider particular ordered sets (connected and of small height) and determine the cardinality of the corresponding dual MS - algebra and of its set of fixed points. The remainder of the thesis is devoted to a study of congruences of Ockham algebras and a generalised variety K𝜔 of Ockham algebras that contains all of the Berman varieties K[sub]p,[sub]q. In particular we consider the congruences [sub]i(i = 1, 2,...) defined on an Ockham algebra (L; f) by (x, y) ∊ [sub]i ⇔ fⁱ(x)= fⁱ(y) and show that (L; f) ∊ K𝜔 is subdirectly irreducible if and only if the lattice of congruences of L reduces to the chain 𝜔 = 𝝫₀ ≤ 𝝫₁≤ 𝝫₂≤ … ≤𝝫𝜔<𝞲 Where 𝝫𝜔 = ⌵ [sub]i≥0𝝫i. Finally we obtain a characterisation of the finite simple Ockham algebras.
Thesis, PhD Doctor of Philosophy
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.