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http://dx.doi.org/10.14317/jami.2020.065

PSEUDO P-CLOSURE WITH RESPECT TO IDEALS IN PSEUDO BCI-ALGEBRAS  

MOUSSAEI, HOSSEIN (Department of Mathematics, Shahid Chamran University of Ahvaz)
HARIZAVI, HABIB (Department of Mathematics, Shahid Chamran University of Ahvaz)
Publication Information
Journal of applied mathematics & informatics / v.38, no.1_2, 2020 , pp. 65-77 More about this Journal
Abstract
In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by ApcI, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that Apc{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which ApcI = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.
Keywords
pseudo BCI-algebra; pseudo ideal; pseudo p-closure ideal; complete lattice; closure operation;
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