| 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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