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Ascent and descent of going-down rings for integral extensions
Published online by Cambridge University Press: 17 April 2009
Abstract
The author and Ira J. Papick have termed an integral domain R a going-down ring if R ⊂ T satisfies going-down for each domain T containing R. The present paper investigates conditions which, for an integral extension A ⊂ B of domains, imply that A (respectively B ) is going-down whenever B (respectively A ) is going-down. This explains the “descent” (respectively “ascent”) in the title. Two typical results (the first about descent, the second about ascent) are given next.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 15 , Issue 2 , October 1976 , pp. 253 - 264
- Copyright
- Copyright © Australian Mathematical Society 1976
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