GeneralizationsAny ring can be seen as an [additive category]? with a single object. It is therefore natural to consider arbitrary additive categories to be generalizations of rings. And indeed, many definitions and theorems originally given for rings can be translated to this more general context. Functors between additive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms. |
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