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On Annihilator in Pseudo BCI-algebras.

Authors :
Banderi, Ali
Harizavi, Habib
Source :
Southeast Asian Bulletin of Mathematics. 2021, Vol. 45 Issue 3, p301-315. 15p.
Publication Year :
2021

Abstract

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]

Details

Language :
English
ISSN :
01292021
Volume :
45
Issue :
3
Database :
Academic Search Index
Journal :
Southeast Asian Bulletin of Mathematics
Publication Type :
Academic Journal
Accession number :
151411099