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On pseudo-BCI-algebras

Grzegorz Dymek (2015)

Annales UMCS, Mathematica

The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.

On systems of congruences on principal filters of orthomodular implication algebras

Radomír Halaš, Luboš Plojhar (2007)

Mathematica Bohemica

Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.

On the lattice of deductive systems of a BL-algebra

Dumitru Bu§neag, Dana Piciu (2003)

Open Mathematics

For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.

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