On the Trace of a Permuting Tri-additive Mapping in Left s<sub>&gamma;</sub>-unital &Gamma;-rings

Authors

  • K. K. Dey
  • A. C. Paul Rajshahi University

DOI:

https://doi.org/10.3329/jsr.v3i2.7278

Keywords:

Permuting tri-additive mappings, Skew-commuting mappings, Skew-centralizing mappings, Commuting mappings.

Abstract

Let M be 2 and 3 torsion-free left sΓ-unital Γ-rings. Let D: M ×M ×M ® M be a permuting tri-additive mapping with the trace d(x) = D(x,x,x). Let σ: M ® M be an endomorphism and τ: M ® M an epimorphism. The objective of this paper is to prove the following: a) If d is (σ,τ)-skew commuting on M, then D = 0;   b) If d is (τ,τ)-skew-centralizing on M, then d is (τ,τ)-commuting on M;  c)  If d is 2-(σ,τ)-commuting on M, then d is (σ,τ)-commuting on M.

Keywords: Permuting tri-additive mappings; Skew-commuting mappings; Skew-centralizing mappings; Commuting mappings.

© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi:10.3329/jsr.v3i2.7278                 J. Sci. Res. 3 (2), 331-337 (2011)

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Author Biography

A. C. Paul, Rajshahi University

Dr. Akhil Chandra Paul

Professor

Department of Mathematics

Rajshahi University

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Published

2011-04-28

How to Cite

Dey, K. K., & Paul, A. C. (2011). On the Trace of a Permuting Tri-additive Mapping in Left s<sub>&gamma;</sub>-unital &Gamma;-rings. Journal of Scientific Research, 3(2), 331–337. https://doi.org/10.3329/jsr.v3i2.7278

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Section

Section A: Physical and Mathematical Sciences