Applied Categorical Structures

, Volume 3, Issue 2, pp 139–149 | Cite as

Ideals, radicals, and structure of additive categories

  • Ross Street


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 anoether full, faithful functor into a category of modules over a division ringoid.

Mathematics subject classifications (1991)

18E05 16A20 16A40 

Key words

Additive category semiprimitive ring artinian simple Jacobson radical density arguments 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Ross Street
    • 1
  1. 1.Mathematics DepartmentMacquarie UniversityAustralia

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