i've never seen this notation before! by Q(R,T) do you mean the localization of at ? in this case just choose any elements of then is the unity of Q(R,T).

we, as you mentioned yourself, assume that so saying something like "every non-zero element of " is not necessarily! if R has no unity, the inverse of an elementb) In Q(R,T) every nonzero element of T is a unit.

in Q(R,T) is if R has a unity, then the inverse of in Q(R,T) is simply

4 elements. note that in we have and in fact

c) how many elements are there in the ring Q(Z4, {1,3})

i'm not sure what this part is trying to say! is it claiming that is isomorphic to a subring of ??

d) describe the ring Q(3Z, {6^N | N is in Z+}) by describing a subring of R to which it is isomorphic.

Thanks