General Wedderburn Theorems
The study of endomorphism rings is important both in the study of modules and in the study of abstract rings. It is important in the study of modules because many properties of a module are characterizable by properties of its endomorphism ring. Indeed, some modules over certain rings are determined by their endomorphism rings, which is a way of saying that the modules are isomorphic if and only if their endomorphism rings are isomorphic qua rings. This is true for vector spaces. It is important for the study of rings, since some rings, even those abstractly defined, can be embedded in a ring of endomorphisms of a relatively “nice” module, for example, a vector space.
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