Ideals, radicals, and structure of additive categories
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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 wordsAdditive category semiprimitive ring artinian simple Jacobson radical density arguments
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