English Dictionary

multiplicative subset

名詞

(commutative algebra) A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation.

日本語の意味

環の単位元（1）を含み、環の乗法演算に関して閉じている部分集合。すなわち、任意の2要素の積が再びその部分集合に属するという性質を持つ集合。

To construct the localization of a ring, algebraists invert every element of a multiplicative subset and adjoin the resulting inverses.

環の局所化を構成するために、代数学者は単位元を含み乗法に関して閉じている部分集合のすべての元を逆元にして、その逆元を付け加える。

意味（1）

(commutative algebra) A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation.

If P is a proper prime ideal of a ring and M is the set complement, w.r.t. the ring, of P, then M is a multiplicative subset.

multiplicative subsets （ plural ）