2018/08/28 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13B22 #14B05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A30 #Rings, Modules, and Algebras #Secondary 13A50
paper · pdf · doi:10.48550/arxiv.1808.09130
openalex publication_date 2018/08/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let (A,\mathfrakm) be an excellent normal domain of dimension two. We define an \mathfrakm-primary ideal I to be a pg-ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. When A contains an algebraically closed field k ≅ A/\mathfrakm 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/\mathfrakm of characteristic zero then also A has pg-ideals. Furthermore product of two pg-ideals is pg.