ring of fractions

Noun

Meaning

ring of fractions (plural rings of fractions)

(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



a

/

b


{\displaystyle a/b}

and



c

/

d


{\displaystyle c/d}

are deemed equivalent if there is a member x of D such that



x
(
a
d
−
b
c
)
=
0


{\displaystyle x(ad-bc)=0}

.

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