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 anoether full, faithful functor into a category of modules over a division ringoid.
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Street, R. Ideals, radicals, and structure of additive categories. Appl Categor Struct 3, 139–149 (1995). https://doi.org/10.1007/BF00877633
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DOI: https://doi.org/10.1007/BF00877633