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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

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Property of a commutative ring that is determined by the prime ideals of the ring

Proposition 1.2.10(a) in "Cohen–Macaulay Rings" by W. Bruns, H.J. Herzog: if $R$ is a Noetherian ring, $I$ an ideal of $R$, and $M$ a finite $R$-module, then $$\operatorname{grade} (I,M)= \inf \{\oper …
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