Open AccessCertain Pairs of Generalized Derivations of Semiprime Rings
Author(s) -
Mehsin Jabel Atteya,
Dalal Resan,
Mesaa Salmaan
Publication year - 2021
Publication title -
magallaẗ kulliyyaẗ al-rāfidayn al-ǧāmi'aẗ al-'ulūm/maǧallaẗ kulliyyaẗ al-rāfidayn al-ǧāmiʻaẗ li-l-ʻulūm
Language(s) - English
Resource type - Journals
eISSN - 2790-2293
pISSN - 1681-6870
DOI - 10.55562/jrucs.v32i2.338
Subject(s) - semiprime ring , centralizer and normalizer , mathematics , invertible matrix , pure mathematics , property (philosophy) , ring (chemistry) , element (criminal law) , center (category theory) , semiprime , combinatorics , discrete mathematics , philosophy , crystallography , prime (order theory) , chemistry , organic chemistry , epistemology , political science , law
Let R be a semiprime ring with the cancellation property ,U be a set of R, (D,d) and (G,g) be generalized derivations of R ,if R admits to satisfied some conditions ,where d acts as a left centralizer (resp.g acts as a left centralizer).Then there exist idempotents ϵ1, ϵ 2, ϵ 3 C and an invertible element λ C such that ϵ iϵ j= 0, for i≠j, ϵ 1+ ϵ 2+ ϵ 3 =1,and ϵ 1f(x)=λϵ 1g(x), ϵ 2g(x)= 0, ϵ 3f(x)= 0 hold for all x U. (*)During our paper we will using (*)for denoted to above result.