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In EGA IV2, Def. 3.2.4, Grothendieck defines a quasicoherent sheaf over a locally Noetherian scheme to be "irredondant" if it has a unique associated point. Presumeably, a module over a Noetherian ring is irredondant if it has a unique associated prime. However, googling gives no relevant results for "irredundant sheaf" or "irredundant module" (which I can understand, since it is rather a peculiar name).

How is this term usually rendered into English? Ideally, answers should include at least one reference to a text or paper using this term.

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Wikipedia calls a module over a commutative Noetherian ring with only one associated prime a coprimary module. I don't recall hearing this terminology elsewhere, but it is certainly common to call a submodule $N$ of $M$ a primary submodule if $M/N$ is coprimary.

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  • $\begingroup$ Googling this gives enough relevant hits to make me think that it's probably the standard term (if there is one). $\endgroup$
    – Charles Staats
    Commented Jul 12, 2010 at 18:04
  • $\begingroup$ I'm pretty sure that's what Eisenbud uses as well. $\endgroup$
    – Akhil Mathew
    Commented Jul 12, 2010 at 18:36

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