Extended degree functions and monomial modules

Uwe Nagel, Tim Römer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)3571-3589
Number of pages19
JournalTransactions of the American Mathematical Society
Issue number8
StatePublished - Aug 2006


  • Bounds for degree functions
  • Buchsbaum module
  • Extended degree functions
  • Generic initial module
  • Lexicographic module
  • Sequentially Cohen-Macaulay module

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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