Meaning of k-algebra | Babel Free

Definitions

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

Examples

“A k'''-algebra A with ring homomorphism ϕ:k→A is a k-vector space with scalar multiplication (i.e., action of k upon A): λ·a=ϕ(λ)a where λ∈k,a∈A.”

CEFR level