Really, this question comes down to listing propeties that are preserved by ring isomorphisms. Off the top of my head, I can think of:
- cardinality of the ring
- commutativity
- the order of elements
- being a UFD, PID, field etc.
What else is there?
2026-03-26 14:20:33.1774534833
Listing methods to prove that two rings are not isomorphic
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Pretty much anything one can think of, in particular literally anything first-order expressible ("Isomorphic structures are a fortiori elementarily equivalent")