Ideals, radicals, and structure of additive categories

Ross Street*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)

    Abstract

    Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid.

    Original languageEnglish
    Pages (from-to)139-149
    Number of pages11
    JournalApplied Categorical Structures
    Volume3
    Issue number2
    DOIs
    Publication statusPublished - Jun 1995

    Keywords

    • Additive category
    • artinian
    • density arguments
    • Jacobson
    • Mathematics subject classifications (1991): 18E05, 16A20, 16A40
    • radical
    • semiprimitive ring
    • simple

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