Von Neumann, J. (1936) On Regular Rings. Proceedings of the National Academy of Sciences of the United States of America, 22, 707-713.
has been cited by the following article:
- TITLE: On Semi π-Regular Local Ring
- AUTHORS: Zubayda M. Ibraheem, Raghad A. Mustafa, Maha F. Khalf
- KEYWORDS: Local, Ring, Semi π-Regular
JOURNAL NAME: Open Access Library Journal
Oct 12, 2018
A ring R is said to be a right (left) semi π-regular local ring if and only if for all a in R, either a or (1-a) is a right (left) semi π-regular element. The purpose of this paper is to give some characterization and properties of semi π-regular local rings, and to study the relation between semi π-regular local rings and local rings. From the main results of this work: 1) Let R be a semi π-regular reduced ring. Then the idempotent associated element is unique. 2) Let R be a ring. Then R is a right semi π-regular local ring if and only if either r(an) or r((1-a)n) is direct summand for all a∈R and n∈Z . If R is a local ring with r(an) r(a) for all a∈R and n∈Z , then R is a right semi π-regular local ring.