English Dictionary

k-algebra

名詞

(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.

日本語の意味

体 k 上の代数：体 k から単射の環準同型によって、その像が環の中心に含まれ、かつ体の単位元が環の単位元に対応する、単位元を持つ環としての代数。

The representation theory of a finite-dimensional k-algebra reveals much about its module category.

有限次元の体k上の代数の表現論は、その加群圏について多くを明らかにする。

意味（1）

(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 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.

k-algebras （ plural ）