2026-06-27T23:02:10Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/583242023-08-27T16:28:08Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Ruiz Sancho, Jesús María
2023-06-20T18:41:37Z
2023-06-20T18:41:37Z
1989-08-01
0021-8693
10.1016/0021-8693(89)90129-4
https://hdl.handle.net/20.500.14352/58324
http://www.sciencedirect.com/science/article/pii/0021869389901294
http://www.sciencedirect.com
In this note, the author proves, in the context of excellent rings, two results on chains of specializations in the real spectrum and some corollaries about real dimension. The first result (Theorem I) is the following: let α0 be a point of SpecrA of dimension d0 in the closure of a constructible set S of real dimension d at α0; then there exists a chain of strict specializations of exactly d points αd→⋯→α0 entirely contained in S, specializing to α0. This theorem is in fact a full generalization, in that context, of the "curve selection lemma'' (which corresponds to the existence of α1 in the case d0=1). The second result (2.1) says that if A is an excellent local domain, any ordering of the fraction field inducing an ordering in the residue field extends to a "formal branch'' (that is, an irreducible component of the completion Â). Both results are simultaneously proved by induction on the Krull dimension of A [see also the author, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 2, 67–69].
eng
A dimension theorem for real spectra
journal article
URL
https://docta.ucm.es/bitstreams/c3838584-b1c1-415b-a854-99a260db1d54/download
File
MD5
7da0325b83ccbe1f56abf386a9a3a841
360636
application/pdf
RuizSancho19.pdf
URL
https://docta.ucm.es/bitstreams/ebfdb2f5-0a3d-4203-858e-b6c7a69d3e90/download
File
MD5
7ecf939657acbd8a121df1e5aca3bf6d
14488
text/plain
RuizSancho19.pdf.txt