TY - JOUR
T1 - Liaison classes of modules
AU - Nagel, Uwe
N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.
PY - 2005/2/1
Y1 - 2005/2/1
N2 - We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules. As a consequence, we show that the intermediate cohomology modules and properties like being perfect, Cohen-Macaulay, Buchsbaum, or surjective-Buchsbaum are preserved in even module liaison classes. Furthermore, we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one.
AB - We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules. As a consequence, we show that the intermediate cohomology modules and properties like being perfect, Cohen-Macaulay, Buchsbaum, or surjective-Buchsbaum are preserved in even module liaison classes. Furthermore, we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one.
UR - http://www.scopus.com/inward/record.url?scp=12144265944&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=12144265944&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2004.09.022
DO - 10.1016/j.jalgebra.2004.09.022
M3 - Article
AN - SCOPUS:12144265944
SN - 0021-8693
VL - 284
SP - 236
EP - 272
JO - Journal of Algebra
JF - Journal of Algebra
IS - 1
ER -