Constructing big indecomposable modules
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- by Andrew Crabbe and Janet Striuli PDF
- Proc. Amer. Math. Soc. 137 (2009), 2181-2189 Request permission
Abstract:
Let $R$ be local Noetherian ring of depth at least two. We prove that there are indecomposable $R$-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.References
- M. Auslander, Finite type implies isolated singularity, Orders and their applications (Oberwolfach, 1984) Lecture Notes in Math., vol. 1142, Springer, Berlin, 1985, pp. 1–4. MR 812487, DOI 10.1007/BFb0074789
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- R.-O. Buchweitz, G.-M. Greuel, and F.-O. Schreyer, Cohen-Macaulay modules on hypersurface singularities. II, Invent. Math. 88 (1987), no. 1, 165–182. MR 877011, DOI 10.1007/BF01405096
- Andrew Crabbe, Daniel Katz, Janet Striuli, and Emanoil Theodorescu, Hilbert polynomials for the controvarient functor, preprint (2007).
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- Anders J. Frankild, Sean Sather-Wagstaff, and Roger Wiegand, Ascent of module structures, vanishing of ext, and extended modules, Mich. J. Math., to appear.
- W. Hassler, R. Karr, L. Klingler, and R. Wiegand, Large indecomposable modules over local rings, J. Algebra 303 (2006), no. 1, 202–215. MR 2253659, DOI 10.1016/j.jalgebra.2006.05.016
- Wolfgang Hassler, Ryan Karr, Lee Klingler, and Roger Wiegand, Big indecomposable modules and direct-sum relations, Illinois J. Math. 51 (2007), no. 1, 99–122. MR 2346189
- Wolfgang Hassler, Ryan Karr, Lee Klingler, and Roger Wiegand, Indecomposable modules of large rank over Cohen-Macaulay local rings, Trans. Amer. Math. Soc. 360 (2008), no. 3, 1391–1406. MR 2357700, DOI 10.1090/S0002-9947-07-04226-2
- Wolfgang Hassler and Roger Wiegand, Big indecomposable mixed modules over hypersurface singularities, Abelian groups, rings, modules, and homological algebra, Lect. Notes Pure Appl. Math., vol. 249, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 159–174. MR 2229110, DOI 10.1201/9781420010763.ch15
- Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, New York-Berlin, 1980. Reprint of the 1974 original. MR 600654
- Daniel Katz and Emanoil Theodorescu, On the degree of Hilbert polynomials associated to the torsion functor, Proc. Amer. Math. Soc. 135 (2007), no. 10, 3073–3082. MR 2322736, DOI 10.1090/S0002-9939-07-08879-X
- Lee Klingler and Lawrence S. Levy, Representation type of commutative Noetherian rings. I. Local wildness, Pacific J. Math. 200 (2001), no. 2, 345–386. MR 1868696, DOI 10.2140/pjm.2001.200.345
- Lee Klingler and Lawrence S. Levy, Representation type of commutative Noetherian rings. I. Local wildness, Pacific J. Math. 200 (2001), no. 2, 345–386. MR 1868696, DOI 10.2140/pjm.2001.200.345
- Lee Klingler and Lawrence S. Levy, Representation type of commutative Noetherian rings. III. Global wildness and tameness, Mem. Amer. Math. Soc. 176 (2005), no. 832, viii+170. MR 2147090, DOI 10.1090/memo/0832
- Vijay Kodiyalam, Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), no. 3, 757–764. MR 1156471, DOI 10.1090/S0002-9939-1993-1156471-5
- Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
- Joseph J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, vol. 85, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 538169
Additional Information
- Andrew Crabbe
- Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
- Address at time of publication: Department of Mathematics, Syracuse University, Syracuse, New York 13210
- Email: amcrabbe@syr.edu
- Janet Striuli
- Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
- Address at time of publication: Department of Mathematics, Fairfield University, Fairfield, Connecticut 06824
- Email: jstriuli@mail.fairfield.edu
- Received by editor(s): May 8, 2008
- Received by editor(s) in revised form: August 29, 2008
- Published electronically: January 26, 2009
- Additional Notes: The second author was partially supported by NSF grant DMS 0201904
- Communicated by: Bernd Ulrich
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2181-2189
- MSC (2000): Primary 13H10, 13C14, 13E05
- DOI: https://doi.org/10.1090/S0002-9939-09-09760-3
- MathSciNet review: 2495250