k-algebra

noun

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.”

Similar
algebra over a field
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Meanings

nounk-algebra (plural k-algebras)

plural k-algebras

  1. algebraAn 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: algebra over a field

Synonyms & antonyms

nounAn 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.

Similar
algebra over a field
Also see
algebra over a field
Cite this entry
APA

k-algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/k-algebra

MLA

“k-algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/k-algebra. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “k-algebra,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/k-algebra.

Source: k-algebra on Wiktionary, CC BY-SA 4.0.