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On the category of pseudo-BCI-algebras

Dymek G.

Demonstratio Mathematica

2013

Vol. 46, nr 4

631--644

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.

Atoms and ideals of pseudo-BCI-algebras

Dymek G.

Commentationes Mathematicae

2012

Vol. 52, [Z] 1

73-90

The main subject of the paper are atoms and ideals of a pseudo-BCI-algebra. Many different characterizations of them are given. Some connections between ideals and subalgebras are presented. Conditions for the set At(X) of atoms of a pseudo-BCI-algebra X to be an ideal of X are established.