ring of fractions

ring of fractions (plural rings of fractions)

1. (algebra) 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 ${\displaystyle a/b}$ and ${\displaystyle c/d}$ are deemed equivalent if there is a member x of D such that ${\displaystyle x(ad-bc)=0}$.

• field of fractions
• total ring of fractions
• localization