k-algebra

English

Noun

1. Template:Lb An algebra over a field; a Template:L with identity together with an Template:L ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the Template:L of the ring and such that the image of the field’s Template:L is the ring’s unity.

   A k-algebra A with ring homomorphism $\varphi :k\to A$ is a k-vector space with scalar multiplication (i.e., action of k upon A): $\lambda \cdot a=\varphi (\lambda )a$ where $\lambda \in k,a\in A$.

Synonyms

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Hypernyms

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Meronyms

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