Question: 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

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:

a. Q(R, T) has unity even if R does not.

b. In Q(R, T), every nonzero element of T is a unit.

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a Because T is nonempty there exists a T Then a a is unity in QR T because a ab c ab a... View full answer

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