RELATIONS OF MULTIPLICATIVE GENERALIZED (α,β)- REVERSE DERIVATION AND α- COMMUTING MAPS

Year 2023, , 41 - 49, 04.07.2023

Barış Albayrak

https://doi.org/10.38061/idunas.1260138

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

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