k-algebra

English

k-algebra (plural k-algebras)

(algebra) 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 ${\\displaystyle \\phi :k\\rightarrow A}$ is a k-vector space with scalar multiplication (i.e., action of k upon A): ${\\displaystyle \\lambda \\cdot a=\\phi (\\lambda )a}$ where ${\\displaystyle \\lambda \\in k,\\ a\\in A}$ .

单词	k-algebra
释义	k-algebra English Noun k-algebra (plural k-algebras) (algebra) 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 ${\\displaystyle \\phi :k\\rightarrow A}$ is a k-vector space with scalar multiplication (i.e., action of k upon A): ${\\displaystyle \\lambda \\cdot a=\\phi (\\lambda )a}$ where ${\\displaystyle \\lambda \\in k,\\ a\\in A}$ . Synonyms algebra over a field Hypernyms ring vector space Meronyms center field unity, identity
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