Mathematics Faculty Articles
Document Type
Article
Publication Date
9-9-2009
Publication Title
Annales de la Faculté des sciences de Toulouse : Mathématiques
ISSN
0240-2963
Volume
19
Issue/No.
S1
First Page
101
Last Page
110
Abstract
Let A be a commutative ring with identity and I an ideal of A. A is said to be I-clean if for every element α∈A there is an idempotent e = e2∈A such that α−e is a unit and αe belongs to I. A filter of ideals, say F, of A is Noetherian if for each I∈F there is a finitely generated ideal J∈F such that J⊆I. We characterize I-clean rings for the ideals 0, n(A), J(A), and A, in terms of the frame of multiplicative Noetherian filters of ideals of A, as well as in terms of more classical ring properties.
NSUWorks Citation
Iberkleid, Wolf and McGovern, Warren William, "Classes of Commutative Clean Rings" (2009). Mathematics Faculty Articles. 40.
https://nsuworks.nova.edu/math_facarticles/40
DOI
10.5802/afst.1277