このエントリーをはてなブックマークに追加
ID 60872
FullText URL
Author
Puthenpurakal, Tony J. Department of Mathematics, IIT Bombay
Abstract
Let (A, m) be an excellent normal domain of dimension two. We define an m-primary ideal I to be a pg -ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If A has infinite residue field then it follows from a result of Rees that the product of two pg ideals is pg . When A contains an algebraically closed field k ∼= A/m then Okuma, Watanabe and Yoshida proved that A has pg -ideals and furthermore product of two pg -ideals is a pg ideal. In this article we show that if A is an excellent normal domain of dimension two containing a field k ∼= A/m of characteristic zero then also A has pg -ideals.
Keywords
pg -ideal
normal Rees rings
Cohen-Macaulay rings
stable ideals
Note
Mathematics Subject Classification. Primary 13A30, 13B22; Secondary 13A50, 14B05.
Published Date
2021-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume63
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
167
End Page
173
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol63/iss1/10