home *** CD-ROM | disk | FTP | other *** search
- Path: sparky!uunet!zaphod.mps.ohio-state.edu!rpi!think.com!yale.edu!ira.uka.de!Germany.EU.net!sbsvax!mpii01044!dubhashi
- From: dubhashi@mpii01044.NoSubdomain.NoDomain (Devdatt Dubhashi)
- Newsgroups: sci.math
- Subject: Euclidean domains
- Keywords: valuation euclidean
- Message-ID: <23741@sbsvax.cs.uni-sb.de>
- Date: 9 Jan 93 13:04:57 GMT
- Sender: news@sbsvax.cs.uni-sb.de
- Organization: Max-Planck-Institut f"ur Informatik
- Lines: 14
-
- >> |>Why there are not other candidates for the Euclidean function?
-
- I'm not sure what the original question was, but hopefully the following
- is not altogether irrelevant!
-
- A Euclidean domain is a ring equipped with a special kind of a valuation -- an
- euclidean valuation, essentially one that makes it amenable to carry out the
- Euclidean algorithm. As usual, one can get a norm out of this by taking a negative
- exponential. Ostrowski's classic theorem asserts that the only possible norms on
- the rationals are the absolute value and the p-adic norms obtained from p-adic
- valuations. I am unaware of of similar general normal form results about
- euclidean valuations on various classes of rings. Perhaps a book on Valuation
- Theory (such as Endler's, which unfortunately is inaccessible to me at present)
- might shed some light on this.
-