Generalized annihilator in pseudo $BCI$-algebras

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Mathematics‎, ‎Shahid Chamran‎ ‎University of Ahvaz‎, ‎Ahvaz‎, ‎Iran

3 Department of Mathematics‎, ‎Payame noor University‎, ‎P.O‎. ‎Box 19395-3697‎, ‎Tehran‎, ‎Iran

Abstract

In this paper‎, ‎for any subsets $D,C$ of a pseudo $BCI$-algebra $A$ the notion of generalized annihilator of $D$ with respect to $C$ and $(\ast,\diamond)$ (resp‎: ‎to $C$ and ($\diamond‎, ‎\ast))$‎, ‎denoted by $(C‎: ‎D)^{(\ast‎, ‎\diamond)}$ (resp‎: ‎$(C‎: ‎D)^{(\diamond‎, ‎\ast)}$) is introduced and its related properties are investigated‎. ‎Also‎, ‎a necessary and sufficient condition for $BCI$-algebra to be p-semisimple or pseudo $BCK$-algebra are given‎. ‎Moreover‎, ‎it is shown that the equation $(C‎: ‎D)^{(\ast,\diamond)} =(C‎: ‎D)^{(\diamond‎, ‎\ast)}$ hold for every p-semisimple $BCI$-algebra‎. ‎Finally‎, ‎it is proved that the set of all involutory ideal‎, ‎denoted by $S_{C}^{(\ast‎ , ‎\diamond)}(A)$ forms a distributive lattice‎.

Keywords

Journal of Algebra and Related Topics

Articles in Press, Corrected Proof
Available Online from 18 April 2026

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