A characterization of Auslander category

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 (R) is a right orthogonal subcategory of some right R-module; and that the Auslander class AC (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.

Anahtar Kelimeler:

Semidualizing module, Auslander class, Bass class

A characterization of Auslander category

Keywords:

Semidualizing module, Auslander class, Bass class,

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