Independence number and minimum degree for the existence of -critical graphs.
As a generalization of filters in lattice implication algebras, the notion of rough filters in lattice implication algebras is introduced, and some of their properties are considered.
We define an ultra -ideal of a lattice implication algebra and give equivalent conditions for an -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra -ideal.
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