关于弱3-Armendariz环(英文)

On Weak 3-Armendariz Rings

引入了弱3-Armendariz环的概念,运用环论的一般方法研究了它们的性质.证明了弱3-Armendariz环的子环和直积是弱3-Armendariz环;环R是弱3-Armendariz环当且仅当对任意n∈N,UTMn(R)(或LTMn(R))是弱3-Arm-endariz环.并给出了环R是弱3-Armendariz环的充要条件.

This paper introduced the concept of weak 3-Armendariz rings, and researched on their properties with the general methods of ring theory. The results prove that the suhrings and direct product of weak 3-Armendariz rings are weak 3-Armendariz rings, and a ring R is weak 3-Armendariz ring if and only if for any n E N, UTMn （R）（or LTM, （R）） are weak 3-Armendariz rings. Sufficient and necessary conditions were given for ring R to be weak 3-Armendariz ring.