The k-Derivation Acting as a k-Endomorphism and as an Anti-k-Endomorphism on Semiprime Nobusawa Gamma Ring

Authors

  • Sujoy Chakraborty Department of Mathematics, Shahjalal University of Science and Technology, Sylhet,
  • Akhil Chandra Paul Department of Mathematics, Rajshahi University, Rajshahi,

DOI:

https://doi.org/10.3329/ganit.v33i0.17663

Keywords:

k-derivation, k-endomorphism, gamma ring, semiprime gamma ring

Abstract

This article defines k-endomorphism and anti-k-endomorphism on ?N-rings, and uses the concept of k-derivation of ?N-rings. Considering M as a semiprime ?N-ring and d as a k-derivation of M, it aims to prove that (i) if d acts as a k-endomorphism on M such that M?M=M and xk(?)x=0 for all x?M and ?? ?, then d=0; and (ii) if d is acting as an anti-k-endomorphism on M such that M?M=M, xk(?)x=0 and k(?)x?=?xk(?) for all x?M and ?? ?, then d=0.

GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 93-101

DOI: http://dx.doi.org/10.3329/ganit.v33i0.17663

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Published

2014-01-13

How to Cite

Chakraborty, S., & Paul, A. C. (2014). The k-Derivation Acting as a k-Endomorphism and as an Anti-k-Endomorphism on Semiprime Nobusawa Gamma Ring. GANIT: Journal of Bangladesh Mathematical Society, 33, 93–101. https://doi.org/10.3329/ganit.v33i0.17663

Issue

Vol. 33 (2013)

Section

Articles

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The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)