ID | 60872 |
FullText URL | |
Author |
Puthenpurakal, Tony J.
Department of Mathematics, IIT Bombay
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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.
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Keywords | pg -ideal
normal Rees rings
Cohen-Macaulay rings
stable ideals
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Note | Mathematics Subject Classification. Primary 13A30, 13B22; Secondary 13A50, 14B05.
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Published Date | 2021-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume63
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 167
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End Page | 173
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol63/iss1/10
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