Name for a module with only one associated prime - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T23:56:43Z http://mathoverflow.net/feeds/question/31584 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/31584/name-for-a-module-with-only-one-associated-prime Name for a module with only one associated prime Charles Staats 2010-07-12T17:32:19Z 2010-07-12T17:46:12Z <p>In EGA IV<sub>2</sub>, Def. 3.2.4, Grothendieck defines a quasicoherent sheaf over a locally Noetherian scheme to be "<em>irredondant</em>" if it has a unique associated point. Presumeably, a module over a Noetherian ring is <em>irredondant</em> 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).</p> <p>How is this term usually rendered into English? Ideally, answers should include at least one reference to a text or paper using this term.</p> http://mathoverflow.net/questions/31584/name-for-a-module-with-only-one-associated-prime/31586#31586 Answer by Robin Chapman for Name for a module with only one associated prime Robin Chapman 2010-07-12T17:46:12Z 2010-07-12T17:46:12Z <p><a href="http://en.wikipedia.org/wiki/Lasker-Noether_theorem" rel="nofollow">Wikipedia</a> calls a module over a commutative Noetherian ring with only one associated prime a <em>coprimary</em> module. I don't recall hearing this terminology elsewhere, but it is certainly common to call a submodule \$N\$ of \$M\$ a <em>primary</em> submodule if \$M/N\$ is coprimary.</p>