ring of fractions

noun

A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0.

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Meanings

nounring of fractions (plural rings of fractions)

plural rings of fractions

  1. algebraA ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0.
Cite this entry
APA

ring of fractions. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/ring%20of%20fractions

MLA

“ring of fractions.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/ring%20of%20fractions. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “ring of fractions,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/ring%20of%20fractions.

Source: ring of fractions on Wiktionary, CC BY-SA 4.0.