【摘要】 若R是*-环，R中每个元素都可以表示成幂零元与投射元的和或者差且二者可交换，则称R是medium诣零*-clean环。文章得到了此环的基本性质，证明了*-环R是medium诣零*-clean环当且仅当R是强*-clean且是弱诣零-clean的，当且仅当R是阿贝尔弱诣零*-clean的，当且仅当R是medium*-clean且J(R)是诣零的。此外，还研究了medium诣零*-clean同态像的基本性质并得到一些等价刻画。更多还原

【Abstract】 A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of a nilpotent with a projection that commute. Fundamenta properties of such *-rings are obtained. It is proved that a *-rings R is medium nil *-clean if and only if R is strongly *-clean and weakly nil clean, while the latter holds true if and only if R is abelian and weakly nil *-clean, if and only if R is medium *-clean and J(R) is nil. Furthermore, some baisc properties of homomorphic images of such ring are explored and some equivalent characterizations are obtained.更多还原