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Generalized annihilator in pseudo $BCI$-algebras | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 29 فروردین 1405 اصل مقاله (167.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.30770.1807 | ||
| نویسندگان | ||
| P. Pirzadeh Ahvazi1؛ H. Harizavi* 2؛ T. Koochakpoor3 | ||
| 1Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| 2Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| 3Department of Mathematics, Payame noor University, P.O. Box 19395-3697, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| BCI-algebra؛ Pseudo BCI-algebra؛ Annihilator؛ Pseudo BCI-ideal؛ Distributive lattice | ||
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