Classes of Commutative Clean Rings

Wolf Iberkleid, Warren William McGovern

    Research output: Contribution to journalArticlepeer-review

    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 = e2A 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 IF there is a finitely generated ideal JF such that JI. 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.

    Original languageAmerican English
    Pages (from-to)101-110
    Number of pages10
    JournalAnnales de la Faculté des sciences de Toulouse : Mathématiques
    Volume19
    Issue numberS1
    DOIs
    StatePublished - Aug 31 2010

    Disciplines

    • Mathematics

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