Ideal extensions of graph algebras
Let and be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of by always exists. We describe (up to isomorphism) all such extensions.
Ideal nil-extensions of semigroups with semimodular congruence lattices.
Ideals and congruence kernels of algebras
Idempotent separating congruences on an orthodox semigroup via the least inverse congruence.
Implication algebras
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....
Induced algebras
Interpolation in congruence permutable algebras
Inverse semirings and their lattice of congruences