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A non-finitely generated algebra of Frobenius maps
Author(s):
Mordechai
Katzman
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2381-2383.
MSC (2010):
Primary 13A35, 13E10
Posted:
March 11, 2010
MathSciNet review:
2607867
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Abstract:
This paper describes an Artinian module over a ring of prime characteristic whose algebra of Frobenius maps is not finitely generated. This settles a question raised by Lyubeznik and Smith.
References:
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- [BH]
- W. Bruns and J. Herzog. Cohen-Macaulay rings. Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1993. MR 1251956 (95h:13020)
- [GS]
- D. Grayson and M. Stillman. Macaulay 2 - a software system for algebraic geometry and commutative algebra, available at http://www.math.uiuc.edu/Macaulay2.
- [K]
- M. Katzman. Parameter-test-ideals of Cohen-Macaulay rings. Compositio Mathematica, 144 (2008), pp. 933-948. MR 2441251 (2009d:13030)
- [LS]
- G. Lyubeznik and K. E. Smith. On the commutation of the test ideal with localization and completion. Transactions of the AMS 353 (2001), no. 8, pp. 3149-3180. MR 1828602 (2002f:13010)
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MSC (2010):
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Additional Information:
Mordechai
Katzman
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email:
M.Katzman@sheffield.ac.uk
DOI:
10.1090/S0002-9939-10-10336-0
PII:
S 0002-9939(10)10336-0
Received by editor(s):
June 5, 2009
Received by editor(s) in revised form:
December 16, 2009
Posted:
March 11, 2010
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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