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Word for one-to-one correspondence between ideals and modules of an algebra

  1. Jul 19, 2011 #1
    I do not know if this is a common/standard construction, so here is my motivation for this question. From http://arxiv.org/abs/1002.1709" [Broken] page 29:

    Is there a word for when there is such a one-to-one correspondence?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 20, 2011 #2
    After rereading this today, I think he might just be saying there is a one-to-one correspondence between ideals and theta-stable U(1)^2-invariant A-modules specifically, not ALL A-modules. So this question probably does not have an answer!
  4. Jul 21, 2011 #3
    For a left R-module M, you can identify certain submodules of M that are similar to that of prime ideals in a ring, R. With that definition there exists conditions on the module M which imply that there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules and prime M-ideals.

    Hope that helps.
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