Manuscript Title:

COMMUTATIVITY OF INTEGRAL DOMAIN INVOLVING PRIME IDEALS OF Γ-RING

Author:

TASLEEM LAL, ZAHEER AHMAD, MUHAMMAD HAMZA, UMBER RANA, MUNTAZIM ABBAS, MOHSIN BILAL

DOI Number:

DOI:10.17605/OSF.IO/S3JVR

Published : 2022-04-23

About the author(s)

1. TASLEEM LAL - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.
2. ZAHEER AHMAD - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.
3. MUHAMMAD HAMZA - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.
4. UMBER RANA - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.
5. MUNTAZIM ABBAS - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.
6. MOHSIN BILAL - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Pakistan.

Full Text : PDF

Abstract

In this paper, the commutativity of quotient Γ-ring has been proved. In this article by applying some algebraic technique (i) [D1(x1), D2(y1)]α – [x1, y1]α ∈P1 (ii) (D1(x1)o D2(y1))α-(x1 oy1)α∈ P1 (iii) [D1(x1), D2(y1)]α-(x1 oy1)α∈P1 (iv) (D1(x1)o D2(y1))α- [x1, y1]α∈P1 ,for all x1, y1∈M, and α∈Γ. Where M be an arbitrary Γ-ring and P1 be a prime ideal. Mainly, the relation between the behavior of Γ-derivation and the structure of this class of Γ-ring has been established.


Keywords

Integral Domain, Prime ideals, Γ-ring