Homological properties of semi-Wakamatsu-tilting modules Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 781-802 https://doi.org/10.4134/BKMS.b190529 Published online February 13, 2020 Printed May 31, 2020 Dajun Liu, Jiaqun Wei Nanjing Normal University; Nanjing Normal University Abstract : For a fixed semi-Wakamatsu-tilting module $_{A}T$, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of $\infty$-$T$-cotorsionfree modules and a subclass of the class of $T$-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained. Keywords : Semi-Wakamatsu-tilting modules, $T$-Auslander class, $T$-Bass class, $\infty$-$T$-cotorsionfree modules, $T$-adstatic modules MSC numbers : Primary 18G35, 16G10; Secondary 18E30, 16E05 Supported by : This work was financially supported by the National Science Foundation of China (Grant No. 11771212) and the National Science Foundation for Distinguished Young Scholars of Jiangsu Province (Grant No. BK2012044) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Downloads: Full-text PDF   Full-text HTML