Mathematical Journal of Okayama University 63巻 1号

2021-01 発行

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.