On functional equation characterizing derivations

被引：1

作者：

Fosner, Maja ^{[1
]}

Marcen, Benjamin ^{[1
]}

Vukman, Joso ^{[2
]}

机构：

[1] Univ Maribor, Fac Logist, Mariborska Cesta 7, Celje 3000, Slovenia

[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

来源：

COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 03期

关键词：

Derivation; functional equation; functional identity; Jordan derivation; Jordan triple derivation; prime ring; JORDAN DERIVATIONS; RINGS;

D O I：

10.1080/00927872.2022.2120616

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the following result. Let R be a prime ring with char(R) not equal 2,3,5,7 and let D : R -> R be an additive mapping satisfying the relation 3D(x(3)) = 2D(x)x(2) + 2x(2)D(x) + xD(x)x + D(x(2))x + xD(x(2)) for all x is an element of R. In this case D is a derivation. This result is related to Herstein's theorem, which states than any Jordan derivation on a prime ring with char (R) not equal 2 is a derivation.

引用

页码：1020 / 1027

页数：8

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