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has been cited by the following article:

• TITLE: Nil 3-Armendariz Rings

  AUTHORS: Eltiyeb Ali, Ayoub Elshokry, Zhongkui Liu

  KEYWORDS: Armendariz Ring; 3-Armendariz Ring; Nil Armendariz Ring; Nil 3-Armendariz Ring

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.9, December 18, 2013

  ABSTRACT: We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , Tn(R) is nil 3-Armendariz ring. Also we prove that a right Ore ring R is nil 3-Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result, we can show that a commutative ring R is nil 3-Armendariz if and only if the total quotient ring of R is nil 3-Armendariz.