On centrally extended Jordan derivations and related maps in rings

被引：4

作者：

Bhushan, Bharat ^{[1
]}

Sandhu, Gurninder Singh ^{[2
]}

Ali, Shakir ^{[3
]}

Kumar, Deepak ^{[1
]}

机构：

[1] Punjabi Univ, Fac Phys Sci, Dept Math, Patiala 147002, India

[2] Patel Mem Natl Coll, Dept Math, Rajpura 140401, India

[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2023年 / 52卷 / 01期

关键词：

Prime ring; semiprime ring; involution; centrally extended Jordan derivation; centrally extended Jordan *-derivation; PRIME; MAPPINGS;

D O I：

10.15672/hujms.1008922

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring and Z(R) be the center of R. The aim of this paper is to define the notions of centrally extended Jordan derivations and centrally extended Jordan *-derivations, and to prove some results involving these mappings. Precisely, we prove that if a 2-torsion free noncommutative prime ring R admits a centrally extended Jordan derivation (resp. centrally extended Jordan *-derivation) 6 : R -> R such that[6(x), x] E Z(R) (resp. [6(x), x*] E Z(R)) for all x E R,where '*' is an involution on R, then R is an order in a central simple algebra of dimension at most 4 over its center.

引用

页码：23 / 35

页数：13

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