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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extended degree functions and monomial modules


Authors: Uwe Nagel and Tim Römer
Journal: Trans. Amer. Math. Soc. 358 (2006), 3571-3589
MSC (2000): Primary 13D40, 13C99; Secondary 13P10, 13H10
Published electronically: December 20, 2005
MathSciNet review: 2218989
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Abstract: The arithmetic degree, the smallest extended degree, and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not Cohen-Macaulay. We compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule. This leads to various bounds and to counterexamples to a conjecture of Gunston and Vasconcelos, respectively. Particular attention is given to the class of sequentially Cohen-Macaulay modules. The results in this case lead to an algorithm that computes the smallest extended degree.


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Additional Information

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email: uwenagel@ms.uky.edu

Tim Römer
Affiliation: FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany
Email: troemer@mathematik.uni-osnabrueck.de

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03848-1
PII: S 0002-9947(05)03848-1
Keywords: Extended degree functions, Buchsbaum module, sequentially Cohen-Macaulay module, generic initial module, lexicographic module, bounds for degree functions
Received by editor(s): June 21, 2004
Received by editor(s) in revised form: August 8, 2004
Published electronically: December 20, 2005
Additional Notes: The first author gratefully acknowledges partial support by a Special Faculty Research Fellowship from the University of Kentucky.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.