On Commutativity of Prime and Semiprime - Rings with Reverse Derivations

Shahed Ali Hamil; Abdulrahman H. Majeed

doi:10.24996/ijs.2019.60.7.15

Authors

Shahed Ali Hamil Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Abdulrahman H. Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2019.60.7.15

Keywords:

Gamma ring, Î³-prime gamma ring, Î³-semiprime gamma ring, Î³-Lie ideal, k- reverse derivation, generalized k- reverse derivation

Abstract

Let M be a weak Nobusawa -ring and Î³ be a non-zero element of Î“. In this paper, we introduce concept of k-reverse derivation, Jordan k-reverse derivation, generalized k-reverse derivation, and Jordan generalized k-reverse derivation of Î“-ring, and Î³-homomorphism, anti-Î³-homomorphism of M. Also, we give some commutattivity conditions on Î³-prime Î“-ring and Î³-semiprime Î“-ring .