Abstract
Let k be a discrete field. A k-algebra is a ring A that is also a vector space over k, satisfying λ(ab) = (λa)b = a(λb) for each λ in k and a, b in A. If A and B are k-algebras, then a homomorphism from A to B is a ring homomorphism that is also a k-linear transformation. The term finite dimensional, when applied to a structure S that is a vector space over k, like a k-algebra, signifies that S is a finite-dimensional vector space over k.
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© 1988 Springer Science+Business Media New York
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Mines, R., Richman, F., Ruitenburg, W. (1988). Finite Dimensional Algebras. In: A Course in Constructive Algebra. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8640-5_9
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DOI: https://doi.org/10.1007/978-1-4419-8640-5_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96640-3
Online ISBN: 978-1-4419-8640-5
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