k-algebra

Noun

 * 1)  An algebra over a field; a  with identity together with an  ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the  of the ring and such that the image of the field’s  is the ring’s unity.
 * A k-algebra A with ring homomorphism $$\phi:k \rightarrow A$$ is a k-vector space with scalar multiplication (i.e., action of k upon A): $$\lambda \cdot a = \phi(\lambda) a$$ where $$\lambda \in k, \ a \in A$$.