What does "k-algebra" mean?

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.

What is a synonym for "k-algebra"?

Common synonyms include: algebra over a field.

K-algebra

noun

noun ·Rare ·Advanced level

Definitions

Noun

1
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.
"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."

Synonyms

All synonyms

algebra over a field

Example

More 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."

More for "k-algebra"

Synonyms Sentences Pronunciation Translate

Next best steps

Find stronger synonyms See usage examples Check pronunciation Browse writing guides

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.