Lifting chains of prime ideals

✍ Scribed by Holger Brenner

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 87 KB
• Volume: 179
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00214-1

✦ Synopsis

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.