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4 votes
0 answers
95 views

List of equivalent conditions for the invariant subalgebra to be polynomial

Let $k$ be a field, $P_n$ the polynomial algebra in $n$ indeterminates, and $G<\operatorname{GL}_n$ a finite group whose order is coprime to the characteristic of $k$, and that acts on $P_n$ by ...
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5 votes
0 answers
788 views

Rings such that torsion-free/flat/projective modules are flat/projective/free

While thinking about this question (and specifically YCor's remarks), I tried to remember what can be said about rings such that every torsion-free module is free, and I could not; and such things, ...
101 votes
31 answers
29k views

Errata for Atiyah–Macdonald

Is there a good list of errata for Atiyah–Macdonald available? A cursory Google search reveals a laughably short list here, with just a few typos. Is there any source available online which lists ...