Associativity of the tensor product

All vector spaces are by default over or . We consider three vector spaces , and . Let be a tensor product of and , and a tensor product of and . The aim is first to show that , together with the mapping:     is a tensor product of , and . Proof:…

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Free associative algebra on a vector space

Vector spaces and associative algebras will be implicitely all on the same field or . Let be a vector space. We wish to build a free associative algebra on . For any natural number , we will note (tensor product times). Each is a vector space. We may form:     An element of can…

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