algebra over a field
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English[edit]
Noun[edit]
algebra over a field (plural algebras over a field)
- (algebra) A vector space (over some field) with an additional binary operation, a vector-valued product between vectors, which is bilinear over vector addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the vector multiplication with respect to the vector addition, which means that such a vector space is also a ring.)