I'm just beginning my study of rings, and I'm wondering if there are some standard ways to show that two rings are not isomorphic. I've studied groups quite a bit and I know some of the ways to show that two groups are not isomorphic (G contains an element of order 2 while G' contains no element of order 2, etc...).(adsbygoogle = window.adsbygoogle || []).push({});

In particular, if for two rings R and R' their associated abelian groups A and A' are isomorphic, what are some ways to use the multiplicative properties of R and R' to show that R and R' are not isomprhic?

The problem I'm working on is to show that the rings 2Z and 3Z are not isomorphic.

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# How to show two rings are not isomorphic

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