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(σ,τ)-*-Jordan ideals in *-prime rings

  • Mohammad Ashraf EMAIL logo and Nazia Parveen

Abstract

Let R be a prime ring with involution , and let σ, τ be endomorphisms on R. For any x,yR, let (x,y)σ,τ=xσ(y)+τ(y)x and Cσ,τ(R)={xRxσ(y)=τ(y)x}. An additive subgroup U of R is said to be a (σ,τ)-right Jordan ideal (resp. (σ,τ)-left Jordan ideal) of R if (U,R)σ,τU (resp. (R,U)σ,τU), and U is called a (σ,τ)-Jordan ideal if U is both a (σ,τ)-right Jordan ideal and a (σ,τ)-left Jordan ideal of R. A (σ,τ)-Jordan ideal U of R is said to be a (σ,τ)--Jordan ideal if U=U. In the present paper, it is shown that if U is commutative, then R is commutative. The commutativity of R is also obtained if (U,U)σ,τCσ,τ(R). Some more results are obtained on the -prime ring with a characteristic different from 2.

MSC 2010: 16W25; 16Y30

Acknowledgements

The authors are indebted to the referee for his/her useful suggestions which improved the paper.

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Received: 2015-03-13
Revised: 2016-10-25
Accepted: 2016-10-31
Published Online: 2017-11-28
Published in Print: 2019-09-01

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