A Pair of Generalized Derivations in Prime, Semiprime Rings and in Banach Algebras

被引：0

作者：

Dhara, Basudeb ^{[1
]}

Rahmani, Venus ^{[2
]}

Sahebi, Shervin ^{[2
]}

机构：

[1] Belda Coll, Dept Math, Paschim Medinipur 721424, WB, India

[2] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran 13185768, Iran

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2021年 / 39卷 / 04期

关键词：

Prime ring; Semiprime ring; Generalized derivation; Utumi quotient ring; Banach algebra;

D O I：

10.5269/bspm.37818

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a prime ring with extended centroid C, I a non-zero ideal of R and n >= 1 a fixed integer. If R admits the generalized derivations H and G such that (H(xy) + G(yx))(n) = (xy +/- yx) for all x, y is an element of I, then one of the following holds: 1. R is commutative; 2. n = 1 and H(x) = x and G(x) = +/- x for all x is an element of R. Moreover, we examine the case where R is a semiprime ring. Finally, we apply the above result to non-commutative Banach algebras.

引用

页码：131 / 141

页数：11

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