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$\gamma$- BCK algebras | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 3 - شماره پیاپی 23، بهمن 2022، صفحه 133-145 اصل مقاله (459.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19322.1234 | ||
| نویسندگان | ||
| Arsham Borumand Saeid* 1؛ M Murali Krishna Rao2؛ R Kumar Kona3 | ||
| 1Department of pure Mathematics, Facultu of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. | ||
| 2Department of Mathematics, Sankethika Institute of Tech. and Management, Visakhapatnam, 530 041, India | ||
| 3Department of Mathematics, GIS, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P., India | ||
| چکیده | ||
| We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations of ring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of $\Gamma-$BCK-algebras as a generalization of BCK-algebras and study $\Gamma-$BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct quotient of $\Gamma-$BCK-algebras. We prove that if $f: M\to L$ be a normal homomorphism of $\Gamma-$BCK-algebras $M$ and $N,$ then $\Gamma-$BCK-algebra $M/N$ is isomorphic to $Im (f)$ where $N =Ker (f).$ | ||
| کلیدواژه‌ها | ||
| ($Gamma-$)BCK-algebra؛ Quotient $Gamma-$BCK-algebra؛ Subalgebra؛ Ideal؛ (Closed؛ Normal) Ideal | ||
| مراجع | ||
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