Right Closed Multiplication sets in Prime Near-Ring -Derivation

Abstract

In  this  paper , we extended the concept given in [1] which they used a semi  group ideal to get the result has been given in [2] . We introduce a new  body which is call it a right closed multiplicative set with zero . This structure  give use  similar results , and  any semi  group ideal satisfy the conditions  of  right  closed  multiplicative  set . We  prove   that  for  any prime  near-ring    and a multiplicative set   , if  , is abelian , then  is abelian  .  These   results    depends   on   many    papers  for  example [3] , [4] , [5] , [6] , [7] , [8] .