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A Lipman’s type construction, glueings and complete integral closure

Published online by Cambridge University Press:  22 January 2016

Valentina Barucci
Valentina Barucci*
Affiliation:
Dipartimento di Matematica Istituto “G. Castelnuovo” Università di Roma “La Sapienza”, Piazzale A. Moro 5, 00185 Roma, Italia
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Given a semilocal 1-dimensional Cohen-Macauly ring A, J. Lipman in [10] gives an algorithm to obtain the integral closure Ā of A, in terms of prime ideals of A. More precisely, he shows that there exists a sequence of rings A = A0 ⊂ A1 ⊂… ⊂ Ai ⊂…, where, for each i, i ≥ 0, Ai+1 is the ring obtained from Ai by “blowing-up” the Jacobson radical ℛ i of Ai+ i.e. Ai+l = ∪n(ℛin:ℛin). It turns out that ∪ {Ai;i≥0} = Ā (cf. [10, proof of Theorem 4.6]) and, if Ā is a finitely generated A-module, the sequence {Ai; i ≥ 0} is stationary for some m and Am = Ā, so that

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 99 - 119
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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