摘要
As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a E R there exist an idempotent e and a regular element r such that a = r ＋ e or a = r - e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean and weakly r-clean rings are equivalent for abelian rings.
As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a E R there exist an idempotent e and a regular element r such that a = r ＋ e or a = r - e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean and weakly r-clean rings are equivalent for abelian rings.
基金
Supported by the National Natural Science Foundation of China(Grant Nos.11401009
11326062)
