a+b and ab are the usual integer addition and multiplication. You can assume that this new operation forms a ring, say R is the set of integers with these operations. Then does R have zero-divisors? And Are R and Z (the integers) isomorphic?

Any help will be appreciated!

  • $\begingroup$ It is a terrible idea to split the question between title and body. Write the entire question in the body please. $\endgroup$ – rschwieb May 2 '16 at 23:08

There's a simple isomorphism $$\varphi : R \to \mathbb{Z},~~z \mapsto 1-z$$ From this it immediately follows that $R$ does not have zero divisors, since $\mathbb{Z}$ does not either.

  • $\begingroup$ Thank you! In addition, Are Z and R isomorphic? $\endgroup$ – Jordy Nelson May 3 '16 at 3:41
  • $\begingroup$ If an isomorphism exists, they're isomorphic. I just gave you an isomorphism. $\endgroup$ – Anon May 3 '16 at 7:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.