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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

On the existence of maximal Cohen-Macaulay modules over $p\,\text{th}$ root extensions

Author(s): Daniel Katz
Journal: Proc. Amer. Math. Soc. 127 (1999), 2601-2609.
MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
Posted: April 15, 1999
MathSciNet review: 1605976
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Abstract | References | Similar articles | Additional information

Abstract: Let $S$ be an unramified regular local ring having mixed characteristic $p > 0$ and $R$ the integral closure of $S$ in a $p$th root extension of its quotient field. We show that $R$ admits a finite, birational module $M$ such that $depth(M) = dim(R)$. In other words, $R$ admits a maximal Cohen-Macaulay module.

References:

[EU]
D. Eisenbud and B. Ulrich, Modules that are finite birational algebras, Illinois Jl. Math 141 No. 1 (1997), 10-15. CMP 97:08

[H]
M. Hochster, Topics in the homological theory of modules over commutative rings, C.B.M.S. Reg. Conf. Ser. in Math., vol. 24, A.M.S., Providence, RI, 1975. MR 51:8096

[HM]
M. Hochster and J.E. McLaughlin, Splitting theorems for quadratic ring extensions, Illinois Jl. Math. 127 No. 1 (1983), 94-103. MR 85c:13015

[Kap]
I. Kaplansky, Commutative Rings II, University of Chicago, Lecture Notes.

[Ka]
D. Katz, $P^{n}$th root extensions in mixed characteristic $p$, preprint (1997).

[KU]
S. Kleiman and B. Ulrich, Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers, Trans. AMS 349 (1997), 4973-5000. MR 98c:13019

[Ko]
J. Koh, Degree $p$ extensions of an unramified regular local ring of mixed characteristic $p >0$, J. of Algebra 99 (1986), 310-323. MR 87j:13027

[MP]
D. Mond and R. Pellikaan, Fitting ideals and multiple points of analytic mappings, Springer Lecture Notes in Mathematics 1414 (1989), 107-161. MR 91e:32035

[R]
P. Roberts, Abelian extensions of regular local rings, Proc AMS 78, No 3 (1980), 307-319. MR 81a:13017

[V]
W. Vasconcelos, Computing the integral closure of an affine domain, Proc. AMS 113 (1991), 633-638. MR 92b:13013

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Additional Information:

Daniel Katz
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: dlk@math.ukans.edu

DOI: 10.1090/S0002-9939-99-04880-7
PII: S 0002-9939(99)04880-7
Received by editor(s): August 26, 1997
Received by editor(s) in revised form: November 26, 1997
Posted: April 15, 1999
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1999, American Mathematical Society




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