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Algebras and Representation Theory

, Volume 21, Issue 6, pp 1369–1380 | Cite as

A Generalized Dade’s Lemma for Local Rings

  • Petter Andreas Bergh
  • David A. Jorgensen
Article
  • 17 Downloads

Abstract

We prove a generalized Dade’s Lemma for quotients of local rings by ideals generated by regular sequences. That is, given a pair of finitely generated modules over such a ring with algebraically closed residue field, we prove a sufficient (and necessary) condition for the vanishing of all higher Ext or Tor of the modules. This condition involves the vanishing of all higher Ext or Tor of the modules over all quotients by a minimal generator of the ideal generated by the regular sequence.

Keywords

Regular sequences Local rings Dade’s Lemma 

Mathematics Subject Classification (2010)

13D02 13D07 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institutt for matematiske fagNTNUTrondheimNorway
  2. 2.Department of mathematicsUniversity of Texas at ArlingtonArlingtonUSA

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