Very long chains of annihilator ideals
β Scribed by Jeanne Wald Kerr
- Book ID
- 112886120
- Publisher
- The Hebrew University Magnes Press
- Year
- 1983
- Tongue
- English
- Weight
- 337 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0021-2172
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π SIMILAR VOLUMES
## Abstract We prove that, e.g., in ^(__Ο__ 3)^(__Ο__ 3) there is no sequence of length W4 increasing modulo the ideal of countable sets (Β© 2010 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
Let R be a ring and let R[x] denote the polynomial ring over R. We study relations between the set of annihilators in R and the set of annihilators in R[x].
We give an elementary proof that for a ring homomorphism A β B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 β β’ β’ β’ β pr in A there exists a chain of prime ideals q0 β β’ β’ β’ β qr in B such that qi β© A = pi.