Mathematical Journal of Okayama University volume63 issue1
2021-01 発行

On pg-ideals

Puthenpurakal, Tony J. Department of Mathematics, IIT Bombay
Publication Date
2021-01
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
Comments
Mathematics Subject Classification. Primary 13A30, 13B22; Secondary 13A50, 14B05.