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.