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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
Posted: December 20, 2005
MathSciNet review: 2218989
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Abstract | References | Similar Articles | Additional Information

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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