unique factorization ring

noun

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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Meanings

noununique factorization ring (plural unique factorization rings)

plural unique factorization rings

  1. ring theoryalgebraA 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.
Cite this entry
APA

unique factorization ring. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/unique%20factorization%20ring

MLA

“unique factorization ring.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/unique%20factorization%20ring. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “unique factorization ring,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/unique%20factorization%20ring.

Source: unique factorization ring on Wiktionary, CC BY-SA 4.0.