$\gamma$- BCK algebras

Document Type : Research Paper

Authors

1 Department of pure Mathematics, Facultu of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

2 Department of Mathematics, Sankethika Institute of Tech. and Management, Visakhapatnam, 530 041, India

3 Department of Mathematics, GIS, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P., India

Abstract

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 $N =Ker (f).$

Keywords

References

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Journal of Mahani Mathematical Research
Volume 11, Issue 3 - Serial Number 23
Special Issue dedicated to Prof. Mashaallah Mashinchi.
November 2022
Pages 133-145

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History

  • Receive Date: 16 April 2022
  • Revise Date: 18 June 2022
  • Accept Date: 25 July 2022

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