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Totally reflexive modules with respect to a semidualizing bimodule

Zhen Zhang, Xiaosheng Zhu, Xiaoguang Yan (2013)

Czechoslovak Mathematical Journal

Let S and R be two associative rings, let S C R be a semidualizing ( S , R ) -bimodule. We introduce and investigate properties of the totally reflexive module with respect to S C R and we give a characterization of the class of the totally C R -reflexive modules over any ring R . Moreover, we show that the totally C R -reflexive module with finite projective dimension is exactly the finitely generated projective right R -module. We then study the relations between the class of totally reflexive modules and the Bass class...

Trisections of module categories

José A. de la Peña, Idun Reiten (2007)

Colloquium Mathematicae

Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying in mod₀ A.

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