Certain Pairs of Generalized Derivations of Semiprime Rings | Zendy

Mehsin Jabel Atteya | Zendy; Dalal Resan | Zendy; Mesaa Salmaan | Zendy

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Certain Pairs of Generalized Derivations of Semiprime Rings

Author(s) -

Mehsin Jabel Atteya,

Dalal Resan,

Mesaa Salmaan

Publication year - 2021

Publication title -

journal of al-rafidain university college for sciences ( print issn 1681-6870 online issn 2790-2293 )

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.

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