English Dictionary

polynomial ring

名詞

(algebra) A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomials (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.

日本語の意味

多項式環（たこうしきかん）：代数における環の一種で、通常は一変数の多項式全体からなり、多くの場合、係数は与えられた環、しばしば体である。一般に、記号K[X]によって表される。

To study algebraic varieties, we start from the polynomial ring K[X] over a field K and then take quotients by ideals to obtain coordinate rings.

代数多様体を研究するために、体K上の1変数の係数を持つ多項式から成る環K[X]を出発点とし、イデアルで割ることで座標環を得ます。

意味（1）

(algebra) A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomials (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.

It then follows that if A is a graded ring over a local ring, A is a homomorphic image of a polynomial ring over a regular local ring. For the sake of brevity, we refer to a graded polynomial ring over a regular local ring simply as a graded polynomial ring.

polynomial rings （ plural ）