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jfiels3
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Homework Statement
Prove that the group Q/Z under addition cannot be isomorphic to the additive group of a commutative ring with a unit element, where Q is the field of rationals and Z is the ring of integers.
Homework Equations
The tools available are introductory-level group theory and ring theory, from a first course in Abstract Algebra.
The Attempt at a Solution
I was thinking that it might be helpful to show that Q/Z has no unit element (since 1 is in Z), and then show that if this were true, then Q/Z must have a unit element. However, I'm not quite sure how to get started, or if I'm even taking a correct approach.