A characterization of Auslander category

Authors : Juxiang SUN

Pages : 793-805

Doi:10.3906/mat-1110-29

View : 9 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we discuss the Bass class and the Auslander class with respect to a semidualizing module over an associative ring. Let SCR be a semidualizing module, we proved that the Bass class BC insert ignore into journalissuearticles values(R); is a right orthogonal subcategory of some right R-module; and that the Auslander class AC insert ignore into journalissuearticles values(S); is a left orthogonal subcategory of the character module of some left S-module. As an application, we introduce the notion of the minimal semidualizing module, and get a one to one correspondence between the isomorphism classes of minimal semidualizing R-modules and maximal classes among coresolving preenvelope classes of Mod R with the same Ext-projective generators in gen* R.
Keywords : Semidualizing module, Auslander class, Bass class