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

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Ideal-like filter on a ring not generated by ring ideals

This does not hold for all commutative rings, but it does hold for Noetherian rings and for valuation rings (assuming the convention that filters don't contain $\emptyset,$ or else $\mathcal{P}(R)$ is …
Elliot Glazer's user avatar