- Natural and Applied Sciences Journal
- Vol: 6 Issue: 1
- RELATIONS OF MULTIPLICATIVE GENERALIZED (α,β)- REVERSE DERIVATION AND α- COMMUTING MAPS
RELATIONS OF MULTIPLICATIVE GENERALIZED (α,β)- REVERSE DERIVATION AND α- COMMUTING MAPS
Authors : Barış Albayrak
Pages : 41-49
Doi:10.38061/idunas.1260138
View : 16 | Download : 26
Publication Date : 2023-07-04
Article Type : Research Article
Abstract :In this paper, properties of ideal I of semiprime ring R with multiplicative generalized (α,β)- reverse derivation with determined not necessarily additive map d is studied. We generalized previous studies for different derivations to multiplicative generalized (α,β)- reverse derivation F. We show that [β(p),d(p)]I=0 for all p∈I or [d(p)],α(p)]I=0 for all p∈I under the given different conditions. Also, we give the relationship between map d and anti-automorphism α of semiprime ring R and automorphism β of semiprime ring R. Under the given different conditions, we examine whether d is α- commuting on ideal I or β- commuting on ideal I and obtain new results.Keywords : Reverse derivation, semiprime ring, commuting map