2004/08/10 by Peter Jørgensen, Peter Jorgensen, Jorgensen, Peter
Mathematics · Physics and Astronomy · #13D07 #13H10 #16E30 #16E65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:13D07 #msc:13H10 #msc:16E30 #msc:16E65
paper · pdf · doi:10.48550/arxiv.math/0408127
18 pages. Paper completely rewritten since version 1 contains an error in the proof of Proposition 2.3
openalex publication_date 2004/08/10 · arxiv created 2005/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete intersection dimension. The result is also proved if A is Gorenstein and has finite Cohen-Macaulay type. Similar results are given for two types of non-commutative rings: Frobenius algebras and complete semi-local algebras.