Homological Aspects of the Dual Auslander Transpose

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.

arXiv comment24 pages, to appear in Forum Mathematicum

Cited by in corpus (3)

• Homological Aspects of the Dual Auslander Transpose II
• Duality Pairs Induced by One-Sided Gorenstein Subcategories
• Cograde conditions and cotorsion pairs