Translation of "Algebraic" in Japanese

An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.

体ｋ上のアフィン代数群とは、ｋ上の可換多元環の圏から群の圏への表現可能な共変関手で、有限生成な多元環によって表現される。