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A Lipman’s type construction, glueings and complete integral closure
Published online by Cambridge University Press: 22 January 2016
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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
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1989
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