Some results on σ-ideal of σ-prime ring

Authors : Selin TÜRKMEN, Neşet AYDIN

Pages : 1147-1156

View : 107 | Download : 12

Publication Date : 2015-10-01

Article Type : Research Paper

Abstract :Let  R  be a  σ -prime ring with characteristic not  2 , Z insert ignore into journalissuearticles values( R );  be the center of  R, I  be a nonzero  σ -ideal of  R, α,β  :  R  →  R  be two automorphisms,  d  be a nonzero  insert ignore into journalissuearticles values( α, β ); -derivation of  R  and  h  be a nonzero derivation of  R.  In the present paper, it is shown that  insert ignore into journalissuearticles values( i );  If  d  insert ignore into journalissuearticles values( I );  ⊂  C α,β  and  β  commutes with  σ  then  R  is commutative.  insert ignore into journalissuearticles values( ii );  Let  α  and  β  commute with  σ.  If  a  ∈  I  ∩  S σ  insert ignore into journalissuearticles values( R );  and  [ d insert ignore into journalissuearticles values( I ); ,a ] α,β  ⊂  C α,β  then  a  ∈  Z insert ignore into journalissuearticles values( R ); .  insert ignore into journalissuearticles values( iii );  Let  α,β  and  h  commute with  σ.  If  dh insert ignore into journalissuearticles values( I ); ⊂ C α,β  and  h insert ignore into journalissuearticles values( I ); ⊂ I  then  R  is commutative.
Keywords : σ prime ring, σ ideal α, β, derivation

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