J-clean环的推广

Generalizations of J-clean Rings

如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环.

A ring R is J-clean(respectively,UJ) if every element(respectively,unit) of R is a sum of an idempotent and an element from the Jacobson radical of R.All J-clean rings are UJ rings.In this paper,we introduce the notion of a GUJ ring,which is a proper generalization of UJ rings.The properties and applications of GUJ rings are discussed.We also investigate rings for which every element is a sum of an idempotent and an element whose power belongs to the Jacobson radical.