中文摘要：

设R是nil-semicommutative的exchange环,证明了如下结论：1）对于R的每个左本原理想P,R/P是除环;2）R是左quasi-duo环;3）若每个非零左R-模有一个极大子模,则R/J（R）是强正则环;4）R/J（R）是强正则环当且仅当R/J（R）是同态半本原环;5）若R的每个素理想是左本原理想,则R为强π-正则环且R/J（R）是强正则环.

英文摘要：

Let Rbe an exchange nil-semicommutative ring.Then 1）R/Pis a division ring for each left primitive ideal Pof R;2）Ris a left quasi-duo ring;3）If every nonzero left R-module has a maximal submodule,then R/J（R）is strongly regular;4）R/J（R）is a strongly regular ring if and only if R/J（R）is a homomorphic semiprimitive ring;5）If every prime ideal of Ris left primitive,then Ris a stronglyπ-regular ring if and only if R/J（R）is a strongly regular ring.