Prove from Exercise 12 that every nonzero commutative ring containing an element a that is not a divisor of 0 can be enlarged to a commutative ring with unity. 

Data from Exercise 12

Let R be a nonzero commutative ring, and let T be a nonempty subset of R closed under multiplication and containing neither 0 nor divisors of 0. Starting with R x T and otherwise exactly following the construction in this section, we can show that the ring R can be enlarged to a partial ring of quotients Q(R, T). Think about this for 15 minutes or so; look back over the construction and see why things still work.