Last Updated
：2025/11/28
unique factorization ring
Noun
Japanese Meaning
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。
（ plural ）
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(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.
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unique factorization ring
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.
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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.
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