Let *R* be a commutative ring containing *regular* elements; that is, elements such that *a* ≠ 0 and *a* is not a zero divisor. In this chapter we show that any commutative ring *R* with regular elements can be embedded in a ring *Q* with unity such that every regular element of *R* is invertible in *Q.* In particular, any integral domain can be embedded in a field. Indeed, by defining the general notion of ring of fractions with respect to a multiplicative subset *S*, we obtain a ring *R*_{s} such that there is a canonical homomorphism from *R* to *R*_{s}. The conditions under which a noncommutative integral domain can be embedded in a division ...

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