Answer by Oliver Braun for Do Noetherian rings have the IBN property?
Let $R\neq\{0\}$ be Noetherian and let $m > n$ be natural numbers. Consider the homomorphism $f ~:~ R^m \to R^n$ given by the projection onto the first $n$ coordinates.The assumption $R^m\cong R^n$...
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I know that commutative rings and division rings have the invariant basis number property. I'm curious what else are there. Do Noetherian rings have the invariant basis number property? If not, what...
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