Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: Daniel Katz
Journal: Proc. Amer. Math. Soc. 127 (1999), 2601-2609
MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
Published electronically: April 15, 1999
MathSciNet review: 1605976
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B21, 13B22, 13H05, 13H15

Retrieve articles in all journals with MSC (1991): 13B21, 13B22, 13H05, 13H15

Additional Information

Daniel Katz
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

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
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society