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

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Finitely generated modules over a complete ring

Is any finitely generated module $M$ over a complete commutative ring $A$ complete? Here complete is with respect to the $I$-adic topology, where $I$ is a given ideal of $A$. Edit: as Luc Guyot …
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