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- Title
Relative Gorenstein Dimensions over Triangular Matrix Rings.
- Authors
Bennis, Driss; El Maaouy, Rachid; García Rozas, Juan Ramón; Oyonarte, Luis
- Abstract
Let A and B be rings, U a (B , A) -bimodule, and T = A 0 U B 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 G C -projective modules over T. As an application, we study when a morphism in T-Mod is a special G C P (T) -precover and when the class G C P (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.
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 21, p2676
- ISSN
2227-7390
- Publication type
Academic Journal
- DOI
10.3390/math9212676