单位正则环

On unit-regular rings.

本文主要研究环的单位正则性 .当 R是一个含幺环时 ,描述了环 R的单位正则性以及与全矩阵环 Mn(R)的单位正则性的等价性 .同时给出完全 0 -单半群环 S=M0 (G;I;Λ;P)当 |I|=|Λ|<+∞且 P可逆时 ,其半群环

The unit\|regularity of a ring with identity is studied. When \$R\$ is a ring with identity, the unit\|regularity of a ring \$R\$ is characterzed and it is proved that the unit\|regularity of \$R\$ is equivalent to that of the full matrix ring \$M\-n(R)\$. For a completely 0\|simple semigroup ring \$S=M\+0(G;I;Λ;P)\$ with \$|I|=|Λ|<+∞\$ and invertible \$P\$, the unit\|regularity of \$RS\$ is characterized.