On the existence of maximal Cohen-Macaulay modules over $p$th root extensions
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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
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Additional Information
- Daniel Katz
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- Email: dlk@math.ukans.edu
- Received by editor(s): August 26, 1997
- Received by editor(s) in revised form: November 26, 1997
- Published electronically: April 15, 1999
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2601-2609
- MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
- DOI: https://doi.org/10.1090/S0002-9939-99-04880-7
- MathSciNet review: 1605976