Fine环的一类推广

A kind of generalization of fine rings

称R是fine环,如果R中任意非零元素均可表示为一个可逆元与一个幂零元之和。作为fine环的一类推广,本文引入J^(#)-fine环的概念,研究了J#-fine环的基本性质及其与相关环类的关系,讨论了矩阵扩张的J^(#)-fine性质,证明了J^(#)-fine环上的任意矩阵环均是J^(#)-fine的.

A ring R is fine if every nonzero element of R is the sum of a unit and a nilpotent.We introduce the concept of J#-fine rings as a generalization of fine rings,and study basic properties of J^(#)-fine rings and the relationship between J^(#)-fine rings and rings which associate with J^(#)-fine rings.We discuss the J^(#)-fineness of matrix expansion and prove that any matrix rings over J^(#)-fine rings are J^(#)-fine.