On Annihilator in Pseudo BCI-algebras.

In this paper, the annihilator of an arbitrary subset of a pseudo BCI-algebra is defined and some related properties are studied. Applying the annihilator concept, some necessary and sufficient conditions for a pseudo BCI-algebra to be p-semisimple are established. Also, the normal pseudo BCI-ideal is defined and studied. The relation between normal pseudo BCI-ideals and pseudo BCK-algebras is discussed. Finally, the involutory pseudo BCI-ideal is defined and it is shown that if {0} is a normal pseudo BCI-ideal then the set of all involutory pseudo BCI-ideals forms a complete and complemented lattice. [ABSTRACT FROM AUTHOR]