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

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Natural and Applied Sciences Journal
Volume: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

Pages : 41-49

View : 104 | Download : 34

Publication Date : 2023-07-04

Article Type : Research Paper

Abstract :In this paper, properties of ideal I of semiprime ring R with multiplicative generalized insert ignore into journalissuearticles values(α,β);- reverse derivation with determined not necessarily additive map d is studied. We generalized previous studies for different derivations to multiplicative generalized insert ignore into journalissuearticles values(α,β);- reverse derivation F. We show that [βinsert ignore into journalissuearticles values(p);,dinsert ignore into journalissuearticles values(p);]I=0 for all p∈I or [dinsert ignore into journalissuearticles values(p);],αinsert ignore into journalissuearticles values(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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