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Lifting chains of prime ideals to paravaluation rings

✍ Scribed by David E. Dobbs

Publisher: Springer Milan
Year: 2000
Tongue: Italian
Weight: 59 KB
Volume: 49
Category: Article
ISSN: 0009-725X
DOI: 10.1007/bf02904237

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We give an elementary proof that for a ring homomorphism A → B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 ⊂ • • • ⊂ pr in A there exists a chain of prime ideals q0 ⊂ • • • ⊂ qr in B such that qi ∩ A = pi.

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