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Modules and Vector Spaces
Another important algebraic structure is that of a module over a ring, in particular, a vector space over a division ring or a field. Till now, we have come across groups and rings, where one or two binary operations are involved. Modules are concerned with one binary operation and several binary operations, one corresponding to each element in the ring. Consider an abelian group (M, +) and let R = End(M, +), the set of all endomorphisms of (M, +). It is well known that R is a ring under point-wise addition and composition of mappings ...
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