Lifting chains of prime ideals
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Holger Brenner
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Article
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2003
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Elsevier Science
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English
โ 87 KB
We give an elementary proof that for a ring homomorphism A โ B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 โ โข โข โข โ pr in A there exists a chain of prime ideals q0 โ โข โข โข โ qr in B such that qi โฉ A = pi.