Usually means: Ideal not contained in larger ideal.
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We found 7 dictionaries that define the word maximal ideal:

General (4 matching dictionaries)
  1. maximal ideal: Wiktionary
  2. maximal ideal: Infoplease Dictionary
  3. maximal ideal: Dictionary.com
  4. Maximal ideal: Wikipedia, the Free Encyclopedia

Computing (1 matching dictionary)
  1. maximal ideal: Encyclopedia

Science (2 matching dictionaries)
  1. Maximal Ideal: Eric Weisstein's World of Mathematics
  2. maximal ideal, maximal ideal: PlanetMath Encyclopedia

Definitions from Wiktionary (maximal ideal)

noun:  (algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).

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