-σ-biderivations on *-rings

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Lal Shateri T.

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ISSN: 2588-4824

Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:5 | Issue:22 Page(s): 13-18

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Title

-σ-biderivations on *-rings

Author(s)

Lal Shateri T. | Issue Writer Certificate

Keywords

Prime ring

semiprime ring

*-ring

*-biderivation

*-σ-biderivation

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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APA: Copy

Lal Shateri, T.. (2020). -σ-biderivations on *-rings. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(22 ), 13-18. SID. https://sid.ir/paper/950752/en

Vancouver: Copy

Lal Shateri T.. -σ-biderivations on *-rings. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;5(22 ):13-18. Available from: https://sid.ir/paper/950752/en

IEEE: Copy

T. Lal Shateri, “-σ-biderivations on *-rings,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 22 , pp. 13–18, 2020, [Online]. Available: https://sid.ir/paper/950752/en

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