Congruence kernels in Ockham algebras

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We consider, in the context of an Ockham algebra , the ideals I of L that are kernels of congruences on . We describe the smallest and the largest congruences having a given kernel ideal, and show that every congruence kernel is the intersection of the prime ideals P such that , , and . The congruence kernels form a complete lattice which in general is not modular. For every non-empty subset X of L, we also describe the smallest congruence kernel to contain X, in terms of which we obtain necessary and sufficient conditions for modularity and distributivity. The case where L is of finite length is highlighted.
Original languageEnglish
Pages (from-to)55-65
JournalAlgebra Universalis
Issue number1
Publication statusPublished - May 2017


  • Ockham algebra
  • congruence
  • kernel ideal


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