Question: With reference to Exercise 12, describe the ring Q(Z, {2 n |n Z + }), by describing a subring of R to which it
With reference to Exercise 12, describe the ring Q(Z, {2n |n ∈ Z+}), by describing a subring of R to which it is isomorphic.
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. In particular, show the following:
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