Commutatively of Prime and Semiprime ?-Rings with Symmetric BI-Derivations

Authors

  • Kalyan Kumar Dey Department of Mathematics, University of Rajshahi, Rajshahi-6205
  • Akhil Chandra Paul Department of Mathematics, University of Rajshahi, Rajshahi-6205

DOI:

https://doi.org/10.3329/ganit.v34i0.28551

Keywords:

?-ring, derivation, bi-derivation, commutativity

Abstract

Let M be a ?-ring and let D: M x M ->M be a symmetric bi-derivation with the trace d: M -> M denoted by d(x) = D(x, x) for all x?M. The objective of this paper is to prove some results concerning symmetric bi-derivation on prime and semiprime ?-rings. If M is a 2-torsion free prime ?-ring and D ? 0 be a symmetric bi-derivation with the trace d having the property d(x)?x - x?d(x) = 0 for all x?M and ???, then M is commutative. We also prove another result in ?-rings setting analogous to that of Posner for prime rings.

GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 27-33

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Author Biography

Kalyan Kumar Dey, Department of Mathematics, University of Rajshahi, Rajshahi-6205



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Published

2016-06-28

How to Cite

Dey, K. K., & Paul, A. C. (2016). Commutatively of Prime and Semiprime ?-Rings with Symmetric BI-Derivations. GANIT: Journal of Bangladesh Mathematical Society, 34, 27–33. https://doi.org/10.3329/ganit.v34i0.28551

Issue

Vol. 34 (2014)

Section

Articles

License

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