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Homological aspects of the dual Auslander transpose

Authors
  • Tang, Xi
  • Huang, Zhaoyong
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Sep 09, 2014
Volume
27
Issue
6
Pages
3717–3743
Identifiers
DOI: 10.1515/forum-2013-0196
Source
De Gruyter
Keywords
License
Yellow

Abstract

As a dual of the Auslander transpose of modules, we introduce and study the cotranspose of modules with respect to a semidualizing module C. Then using it we introduce n-C-cotorsionfree modules, and show that n-C-cotorsionfree modules possess many dual properties of n-torsionfree modules. In particular, we show that n-C-cotorsionfree modules are useful in characterizing the Bass class and investigating the approximation theory for modules. Moreover, we study n-cotorsionfree modules over Artin algebras and answer negatively an open question of Huang and Huang posed in 2012.

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