Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2019.03.28
  • Accepted : 2019.10.11
  • Published : 2020.01.30
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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.

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References

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