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.
|Publication status||Published - May 2017|
- Ockham algebra
- kernel ideal