杭州师范大学学报（自然科学版）
杭州師範大學學報（自然科學版）
항주사범대학학보（자연과학판）
JOURNAL OF HANGZHOU NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2012年
3期
241-244
,共4页
Armendariz环%3-Armendariz环%弱3-Armendariz环
Armendariz環%3-Armendariz環%弱3-Armendariz環
Armendariz배%3-Armendariz배%약3-Armendariz배
Armendariz ring%3-Armendariz ring%weak 3-Armendariz ring
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-Armendariz环.并给出了环R是弱3-Armendariz环的充要条件.
引入瞭弱3-Armendariz環的概唸,運用環論的一般方法研究瞭它們的性質.證明瞭弱3-Armendariz環的子環和直積是弱3-Armendariz環；環R是弱3-Armendariz環噹且僅噹對任意n∈N,UTMn(R)(或LTMn(R))是弱3-Armendariz環.併給齣瞭環R是弱3-Armendariz環的充要條件.
인입료약3-Armendariz배적개념,운용배론적일반방법연구료타문적성질.증명료약3-Armendariz배적자배화직적시약3-Armendariz배；배R시약3-Armendariz배당차부당대임의n∈N,UTMn(R)(혹LTMn(R))시약3-Armendariz배.병급출료배R시약3-Armendariz배적충요조건.
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 subrings 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 ∈ N,UTMn (R)(or LTMn (R)) are weak 3-Armendariz rings.Sufficient and necessary conditions were given for ring R to be weak 3-Armendariz ring.
