k-algebra (pluralk-algebras)

1. (algebra) Analgebra over a field; aring with identity together with aninjectivering homomorphism from a field,k, to the ring such that the image of the field is a subset of thecenter of the ring and such that the image of the field’sunity is the ring’s unity.

   Ak-algebraA with ring homomorphism${\displaystyle \varphi :k\to A}$ is ak-vector space with scalar multiplication (i.e., action ofk uponA):${\displaystyle \lambda \cdot a=\varphi (\lambda )a}$ where${\displaystyle \lambda \in k,a\in A}$.

• algebra over a field

• ring
• vector space

• center
• field
• unity,identity

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