On the vanishing of Ext over formal triangular matrix rings
-
Javad Asadollahi
and
Shokrollah Salarian
Abstract
Let A and B be two rings, M be a left B, right A bimodule and 
be the formal triangular matrix ring. It is known that the category of right T-modules is equivalent to the category Ω of triples (X, Y)f, where X is a right A-module, Y is a right B-module and 
is a right A-homomorphism. Using this alternative description of right T-modules, in the first part of this paper, we study the vanishing of the extension functor ‘Ext’ over T. To this end, we first describe explicitly the structure of (right) T-modules of finite projective (respectively, injective) dimension. Using these results, we shall characterize respectively modules in Auslander's G-class, Gorenstein injective modules, cotorsion modules and tilting and cotilting modules over T. As another application we investigate the structure of the flat covers of right T-modules.
© Walter de Gruyter
Articles in the same Issue
- A summation formula for divisor functions associated to lattices
- On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces
- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
- Homotopy localization of groupoids
- A group-theoretic characterization of the direct product of a ball and a Euclidean space
- Degree-regular triangulations of the double-torus
- Generalized E-algebras over valuation domains
Articles in the same Issue
- A summation formula for divisor functions associated to lattices
- On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces
- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
- Homotopy localization of groupoids
- A group-theoretic characterization of the direct product of a ball and a Euclidean space
- Degree-regular triangulations of the double-torus
- Generalized E-algebras over valuation domains
