2021/06/21 by Bennis, Driss, Maaouy, Rachid El, Rozas, Juan Ramón García +1
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2106.10780
Let A and B be rings, U a (B,A)-bimodule and T=\beginpmatrix A&0 U&B \endpmatrix the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over T using the corresponding ones over A and B. We show that when U is relative (weakly) compatible we are able to describe the structure of GC-projective modules over T. As an application, we study when a morphism in T-Mod has a special GCP(T)-precover and when the class GCP(T) is a special precovering class. In addition, we study the relative global dimension of T. In some cases, we show that it can be computed from the relative global dimensions of A and B. We end the paper with a counterexample to a result that characterizes when a T-module has a finite projective dimension.