The Lattice of Kernel Ideals of a Balanced Pseudocomplemented Ockham Algebra

Studia Logica 102 (1):29-39 (2014)
Abstract
In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ${\fancyscript{I}_{k}(L)}$ of kernel ideals of L is a Heyting lattice that is isomorphic to the lattice of congruences on B(L) where ${B(L) = \{x^* | x \in L\}}$ . In particular, we show that ${\fancyscript{I}_{k}(L)}$ is boolean if and only if B(L) is finite, if and only if every kernel ideal of L is principal
Keywords Congruence  Kernel ideal  Pseudocomplemented algebra  Ockham algebra   Heyting algebra
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DOI 10.1007/s11225-012-9448-1
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