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noetherian

Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • adjective algebra Of a ring in which any ascending chain of ideals eventually starts repeating.
  • adjective algebra Of a module in which any ascending chain of submodules eventually starts repeating.

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

From Emmy Noether

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Examples

  • Hey, Morgan, I’ve got a problem I’ve been wrestling with for a little while this morning, and maybe you can help me out: I’m working on a noetherian scheme, X, with script-I denoting any coherent sheaf of ideals on X (not just the easy ones generated by I where I is a principle ideal).

    Matthew Yglesias » Fun With Tax Deductions 2010

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cross-references (2)

Cross-references

  1. Artinian
  2. ascending chain condition

Comments

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  • travismcdermott commented on the word noetherian

    1943 Ann. Math. 44 690 A ring D is said to be Noetherian if the maximal condition holds for the ideals in D.

    April 13, 2008