单位正则环中的零化子(英文)

Annihilators in Unit-Regular Rings

环R称为单位正则环,如果对任何x∈R,有可逆元u∈R使得x=xux.文章利用零化子刻画了单位正则环,证明了正则环是单位正则环当仅当l(a)∩l(b)=l(d)时,有y∈R使得l(a)∩l(b)=l(a+by),当仅当l(a)=l(b)时,有u∈U(R)使得a=bua.

A ring R is unit-regular provided that for any x E R, there exists an invertible u E R such that x= xux. The paper has characterized the unit-regular ring by means of annihilators, proved that a regular ring R is unit-regular if and only if whenever t（a）∩t（b）=t（d）, there exists y∈R such that l（a）∩t（b）=t（a＋by）, and if and only if whenever t（a）=t（b）, there exists uE U（R） such that a=bua.