Identities with generalized derivations in semiprime rings

Demonstratio mathematica

article

Basudeb Dhara¹  Shakir Ali²  Atanu Pattanayak¹ 

[1] Department of Mathematics, Belda College;Department of Mathematics, Aligarh Muslim University

关键词: prime ring;    semiprime ring;    derivation;    generalized derivation;   

DOI  :  10.1515/dema-2013-0471

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

Let R be a semiprime ring. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F ( xy ) = F ( x ) y + xd ( y ) holds, for all x , y ∈ R . The objective of the present paper is to study the following situations: (1) [ d ( x ), F ( y )] = ±[ x , y ]; (2) [ d ( x ), F ( y )] = ± x ο y ; (3) [ d ( x ), F ( y )] = 0; (4) d ( x )ο F ( y ) = ± x ο y ; (5) d ( x )ο F ( y ) = ±[ x , y ]; (6) d ( x )ο F ( y ) = 0; (7) d ( x ) F ( y )± xy ∈ Z ( R ), for all x , y in some appropriate subset of R .

【 授权许可】

CC BY