Usually means: Ideal containing no nonzero products.
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We found 7 dictionaries that define the word prime ideal:

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

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

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

Definitions from Wiktionary (prime ideal)

noun:  (algebra, ring theory) Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
noun:  In a commutative ring, a (two-sided) ideal I such that for arbitrary ring elements a and b, ab∈I⟹a∈I or b∈I.

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