关于UR-环

On UR-Rings

中文关键词:  clean环  G-clean环  正则环  $(S,2)$-环  UR-环.

英文关键词:clean rings  $G$-clean rings  regular rings  $(S,2)$-rings  UR-rings.

中文摘要:

      一个环称为UR-环如果环中的每个元素是一个可逆元和一个正则元之和.它是正则环、 clean环和(S,2)-环的共同推广.我们研究了这些环之间的关系,推广了clean环和(S,2)-环的一些性质并且考虑了UR-环的扩张问题.

英文摘要:

      A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and $(S,2)$-rings. Some relations of these rings are studied and several properties of clean rings and $(S,2)$-rings are extended. Ring extensions of UR-rings are also investigated.