Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(3): 781-802

Online first article February 13, 2020      Printed May 31, 2020

https://doi.org/10.4134/BKMS.b190529

Copyright © The Korean Mathematical Society.

Homological properties of semi-Wakamatsu-tilting modules

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.

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