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.
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Fang, J., Wang, LB. & Yang, T. The Lattice of Kernel Ideals of a Balanced Pseudocomplemented Ockham Algebra. Stud Logica 102, 29–39 (2014). https://doi.org/10.1007/s11225-012-9448-1
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DOI: https://doi.org/10.1007/s11225-012-9448-1