The Lattice of Kernel Ideals of a Balanced Pseudocomplemented Ockham Algebra

摘要

In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ∮_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 ∈ L}. In particular, we show that ∮_k(L) is boolean if and only if B(L) is finite, if and only if every kernel ideal of L is principal.