Is every commutative ring contained in a field? I imagine the answer to this question is very simple, but I haven't been able to locate it.
Can every commutative ring be imbedded in a field? This seems very plausible to me, for it seems we could just take the "closure" under inverses. 
Thanks!


A commutative ring can be embedded in a field iff it is an integral domain.

Indeed, if a ring can be embedded in a field then it cannot have zero divisors because fields cannot have zero divisors.
Conversely, every integral domain can be embedded in a field, namely, its field of fractions.
