$\gamma$- BCK algebras
We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, 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...
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| Format: | Article |
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Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3360_c7ccfa24ae9c04d2f4a786b35f1867e6.pdf |
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| author | Arsham Borumand Saeid M Murali Krishna Rao R Kumar Kona |
| author_facet | Arsham Borumand Saeid M Murali Krishna Rao R Kumar Kona |
| author_sort | Arsham Borumand Saeid |
| collection | DOAJ |
| description | We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, 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 $N =Ker (f).$ |
| format | Article |
| id | doaj-art-058db3df563b48ea9d684823dce54509 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-058db3df563b48ea9d684823dce545092025-01-07T10:26:23ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052022-11-0111313314510.22103/jmmr.2022.19322.12343360$\gamma$- BCK algebrasArsham Borumand Saeid0M Murali Krishna Rao1R Kumar Kona2Department of pure Mathematics, Facultu of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Department of Mathematics, Sankethika Institute of Tech. and Management, Visakhapatnam, 530 041, IndiaDepartment of Mathematics, GIS, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P., IndiaWe know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, 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 $N =Ker (f).$https://jmmrc.uk.ac.ir/article_3360_c7ccfa24ae9c04d2f4a786b35f1867e6.pdf($gamma-$)bck-algebraquotient $gamma-$bck-algebrasubalgebraideal(closednormal) ideal |
| spellingShingle | Arsham Borumand Saeid M Murali Krishna Rao R Kumar Kona $\gamma$- BCK algebras Journal of Mahani Mathematical Research ($gamma-$)bck-algebra quotient $gamma-$bck-algebra subalgebra ideal (closed normal) ideal |
| title | $\gamma$- BCK algebras |
| title_full | $\gamma$- BCK algebras |
| title_fullStr | $\gamma$- BCK algebras |
| title_full_unstemmed | $\gamma$- BCK algebras |
| title_short | $\gamma$- BCK algebras |
| title_sort | gamma bck algebras |
| topic | ($gamma-$)bck-algebra quotient $gamma-$bck-algebra subalgebra ideal (closed normal) ideal |
| url | https://jmmrc.uk.ac.ir/article_3360_c7ccfa24ae9c04d2f4a786b35f1867e6.pdf |
| work_keys_str_mv | AT arshamborumandsaeid gammabckalgebras AT mmuralikrishnarao gammabckalgebras AT rkumarkona gammabckalgebras |