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arXiv · 1502.03902

Homological Aspects of the Dual Auslander Transpose

Xi Tang·Zhaoyong Huang
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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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Xi Tang, Zhaoyong Huang. 2015-02-13. Homological Aspects of the Dual Auslander Transpose. https://doi.org/10.1515/forum-2013-0196

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