成都大学学报：自然科学版2012，Vol.31Issue(1)：39-42,4.
P-内射的WB-环
Principal-injective WB-rings
摘要
Abstract
Necessary and sufficient conditions under which a principal injective ring＇s equivalence is a WB-ring. It is proved that if R is a nonsingular and principal ring, R just satisfies one of the following con- ditions： （a） R satisfies the ascending chain condition for special left annihilators; （b） R does not contain a direct sum of an infinite number of non-zero principal left ideals; （c） R is a CF-ring; （d） R is a Goldie ring, then the following conditions are equivalent： （1） R is a WB-ring; （2） For any a E R ,there exists or- thogonal ideals I and J such that a = aua = ava, where u ∈R is fight invertible module I and v E R is left invertible module I; （3） For any a E R, there exists orthogonal ideals I, J and e = e^2∈ R such that a = eu = ev,whereu∈R is right invertible module I and v∈R is left invertible module J;（4） If a=b, a, b ∈ R, then there exists orthogonal ideals I, J such that au = ub, av = vb, where u E R is right invert- ible module I and v E R is left invertible module J.关键词
P-内射环/WB-环/正则环/正交理想/特殊左零化子升链条件Key words
P-injective ring/WB-ring/regular ring/orthogonal ideal/the ascending chain condition for spe-cial left annihilators分类
数理科学引用本文复制引用
李艳午,储茂叔,程海霞..P-内射的WB-环[J].成都大学学报：自然科学版,2012,31(1):39-42,4.基金项目
安徽省教育厅优秀青年人才基金 （）
安徽省教育厅自然科学重点项目（KJ2010A126）资助项目. （）
