DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

A.Z. Ansari

Abu Zaid Ansari

Department of Mathematics
Faculty of Science Islamic University of Madinah, K.S.A

email: ansari.abuzaid@gmail.com

Title:

Additive mappings satisfying algebraic identities in semiprime rings

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Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 327-337

Received: 2021-08-29 , Revised: 2022-05-23 , Accepted: 2022-05-23 , Available online: 2023-01-13 , https://doi.org/10.7151/dmgaa.1422

Abstract:

Let R be a k-torsion free semiprime ring. Suppose that F,d:R→R be two additive mappings which satisfy the algebraic identity F(x2n)=F(xn)α(xn)+β(xn)d(xn) for all x∈R, where α and β are automorphisms on R. Then F is a generalized (α,β)-derivation with associated (α,β)-derivation d on R, where k∈{2,n,2n−1}. On the other hand, it is proved that f is a generalized Jordan left (α,β)-derivation associated with Jordan left (α,β)-derivation δ on R if they satisfy the algebraic identity f(x2n)=α(xn)f(xn)+β(xn)δ(xn) for all x∈R together with some restrictions on R.

Keywords:

semiprime rings, generalized (α,β)-derivation, generalized left (α,β)-derivation and additive mappings

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