English Explanatory Dictionary

prime ideal

English dictionary entry

Meanings

noun
  1. Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
  2. 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.

Word forms

prime ideal prime ideals

Etymology

By analogy with the notion of prime number in number theory.

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