Rings of Clean Index 4 and Applications
Journal
Communications in Algebra
Journal Volume
41
Journal Issue
1
Pages
238-259
Date Issued
2013
Author(s)
Zhou, Y.
Abstract
This article is a continuation of the work in [3 Lee , T. K. , Zhou , Y. (2012). Clean index of rings. Comm. Alg. 40(3):807–822.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] on clean index of rings. Motivated by recent work [5 Nicholson , W. K. , Zhou , Y. ( 2004 ). Rings in which elements are uniquely the sum of an idempotent and a unit . Glasg. Math. J. 46 : 227 – 236 .[Crossref], [Web of Science ®] , [Google Scholar]] on uniquely clean rings, the clean index of a ring was introduced in [3 Lee , T. K. , Zhou , Y. (2012). Clean index of rings. Comm. Alg. 40(3):807–822.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] to study the structure of rings, where arbitrary rings of clean indices 1, 2, and 3, respectively, are characterized. In particular, clean rings of clean indices 1, 2, and 3 are determined. In this article, we characterize the rings of clean index 4. As applications, clean rings of clean indices 4, 5, 6 and 7 are completely determined.
SDGs
Type
journal article