noun
Meaning 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.
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided