mjou_063_167_173.pdf 113 KB
Puthenpurakal, Tony J. Department of Mathematics, IIT Bombay
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.
normal Rees rings
Mathematics Subject Classiﬁcation. Primary 13A30, 13B22; Secondary 13A50, 14B05.
Mathematical Journal of Okayama University
Department of Mathematics, Faculty of Science, Okayama University
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