Homological Aspects of the Dual Auslander Transpose

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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.