数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2007年
4期
435-440
,共6页
单位正则%伪相似%零化子
單位正則%偽相似%零化子
단위정칙%위상사%령화자
unit regular ring%pseudo-similarity%annihilator
本文得到了单位正则环的一个新特征,证明了:正则环R为单位正则环当且仅当存在理想I使得(1)R/I为单位正则环;(2)对任何a∈R,存在理想J满足JI=0和a=aua,其中u模J左可逆.作为应用,利用零化子理想刻画了单位正则环.
本文得到瞭單位正則環的一箇新特徵,證明瞭:正則環R為單位正則環噹且僅噹存在理想I使得(1)R/I為單位正則環;(2)對任何a∈R,存在理想J滿足JI=0和a=aua,其中u模J左可逆.作為應用,利用零化子理想刻畫瞭單位正則環.
본문득도료단위정칙배적일개신특정,증명료:정칙배R위단위정칙배당차부당존재이상I사득(1)R/I위단위정칙배;(2)대임하a∈R,존재이상J만족JI=0화a=aua,기중u모J좌가역.작위응용,이용령화자이상각화료단위정칙배.
In this paper, we get a new characterization of unit-regular rings. A regular ring R is unit-regular if and only if there exists an ideal I such that (1) R/I is unit-regular. (2) For each a ∈ R there exist an ideal J such that JI = 0 and a = aua, where u ∈ R is left invertible modulo J. As an application we prove that a regular ring R is unit-regular if and only if there exists an ideal I of R such that R/I and R/r.ann(I) are unit-regular.
