*-σ-biderivations on *-rings

Subject Areas : Statistics

T. Lal Shateri ¹ (ssistant Professor, Department of Mathematics and Computer Sciences (Analysis Research), Hakim Sabzevari University, Sabzevar, Iran)

Received: 2017-11-22 Accepted : 2019-07-06 Published : 2020-01-21

Keywords: * -σ-دواشتقاق, *-حلقه, حلقه نیمه اول, حلقه اول, *-دواشتقاق,

Abstract :

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations for them. He showed every generalized biderivation G of an ideal in a prime ring R is of the form G(x,y)=xay+ybx, where a,b are the elements of the symmetric Martindale ring of quotionts of R. Ali in 2012, studied *-derivations on a *-ring and showed that *-derivations maps to the center of ring.In this paper, we introduce *-biderivations and *-sigma-biderivations on a *-ring. Then some results obtained by Bresar and Ali generalize for these mapping to a class of *-rings. That is, each *-sigma-biderivation is characterized on a prime *-ring and show that each *-biderivation maps to the center of ring.

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