| Abstrakt: |
Let 풥 be a nonzero ideal of a prime ring ℛ and 휂, 휁 be any two mappings on ℛ. A map 풟: ℛ → ℛ is called a multiplicative (generalized) (휂, 휁) reverse derivation if 풟(퓍퓎)=풟(퓎)휂(퓍)+휁(퓎)풹(퓍) for all 퓍, 퓎 ∈ ℛ where 풹: ℛ → ℛ is any map. Let 풟 and ℋ be two multi-plicative (generalized) (휂, 휁) reverse derivation associated with the mapping 풹 and 풽, respectively on ℛ. The purpose of this paper is to investigate some identities of a prime ring ℛ admitting a multi-plicative (generalized) (휂, 휁) reverse derivation 풟 satisfying any one of the properties (i) 풟 (퓎퓍)±휂(퓍퓎)=0 (ii) 풟(퓍퓎)±풟(퓎)풟(퓍)=0 (iii) 풟(퓍퓎)=휂(퓍) ∘ ℋ(퓎) (iv) 풟(퓍퓎)=[휂(퓍), ℋ(퓎)] (v) 풟(퓎퓍)±휂(퓎퓍)=0 (vi) 풟(퓍) 풟 (퓎)±휂(퓎퓍)=0 (vii) 풟(퓍) 풟 (퓎)±휂[ 퓎, 퓍]=0 for all 퓍, 퓎 ∈ 풥. [ABSTRACT FROM AUTHOR] |
