Integral closedness of complete-intersection ideals
This paper studies the problem when a complete intersection ideal I of a noetherian ring A is integrally closed. Main result: The following conditions are equivalent: \((i)\quad \bar I=I;\) \((ii)\quad \overline{I^ n}=I^ n\) for all \(n\geq 1\); \((iii)\quad For\) each \(p\in Ass(A/I)\), the local ring \(A_ p\) is regular and \(\ell ((IA_ p+p^ 2A_ p)/p^ 2A_ p)\geq r-1\), where \(ht(I)=r\). When this is the case, I is unmixed and it is generated by a regular sequence. The second condition is significant because it is equivalent to the normality of the Rees algebra of I, whereas the third condition gives the precise structure of integrally closed complete intersection ideals. The proof is based on the beautiful theory of full ideals recently developed by D. Rees and J. Watanabe\&(see \textit{J. Watanabe}, Nagoya Math. J. 106, 101-111 (1987; Zbl 0623.13012)].
scientific article; zbMATH DE number 4023434