prime ideal

名词 n.
中文释义

英文释义

名词 n.
  1. Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
    — Given a prime number p, there is only a finite number of prime ideals #92;mathfrak#123;p#125; in #92;mathfrak#123;o#125; such that #92;mathfrak#123;p#125;#92;capJ#61;p (they are the prime ideals of #92;mathfrak#123;o#125;p).
  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.

词形变化

prime ideals plural

词源

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