A nonzero element a in a unital ring R is called unit fine if there is a unit u in R such that ua is fine (i.e. a sum of a unit and a nilpotent). A ring all whose elements are unit fine is called accordingly. This turns out to be a new class of simple rings, including the class of fine rings (and so the class of simple Artinian rings). The paper studies unit fine elements and rings. For rings such that 1 is a sum of two units, it is proved that matrix rings over unit fine rings, are unit fine.

中文翻译：

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在单元上的细环

非零元素一个在单位元环- [R被称为单元精细如果有一个单元ü在ř使得UA是细（即，一个单元和幂零的总和）。因此，将所有元素都为单位精细的环称为“环”。事实证明这是一类新的简单环，包括细环类（以及简单的Artinian环类）。本文研究了精细元素和环。对于1是两个单位之和的环，证明单位细环上的矩阵环是单位细的。