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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

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If all localizations of an algebra at primes are of finite type over a field

Let $k$ be a field, and $R$ a $k$-algebra. Suppose that $R_{\mathfrak{p}}$ is a finitely generated $k$-algebra for all prime ideals $\mathfrak{p}$ of $R$. Does this imply that $R$ is also a finitely g …
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