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defines a [[ring homomorphism]] from <math>R</math> into <math>S^{-1}R,</math> which is [[injective function|injective]] if and only if {{mvar|S}} does not contain any zero divisors.
If <math>0\in S,</math> then <math>S^{-1}R</math> is the [[zero ring]] that has only one unique element {{math|0}}
If {{mvar|S}} is the set of all [[zero divisor|regular elements]] of {{mvar|R}} (that is the elements that are not zero divisors), <math>S^{-1}R</math> is called the [[total ring of fractions]] of {{mvar|R}}.
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