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Lie over

verb

Definitions

Verb
  1. 1
    To be deferred to a future occasion. intransitive
  2. 2
    Of a prime ideal q of a ring R' with subring R, to intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p. transitive

    "Let R be a subring of a ring R′ which is integral over R. If P is a prime ideal of R, then there is a prime ideal P′ of R′ that lies over P. Moreover, if P′ and P″ are prime ideals of R′ that lie over P and if P′ ⊆ P″, then P′ = P″."

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