English Dictionary

unique factorization ring

名詞

(algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes.

日本語の意味

任意の非零かつ非単位元が、互いに関連する素数による置換を除いて、一意に（つまり、順序を除くと）素因数（または不可約元）の積に分解できる環のこと。 / 非零で単位でない任意の元が、素因数の積として表現でき、その表現が因子の順序や関連性（同一単位倍による換算）を除いて一意である環。

In ring theory, the structure of a unique factorization ring ensures that every nonzero, nonunit element can be expressed as a product of prime elements uniquely up to order and associates.

環論において、一意分解整域の構造は、任意の非ゼロかつ非単元の元が素元の積として順序および同伴元を除いて一意に表されることを保証する。

意味（1）

(algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes.

unique factorization rings （ plural ）