15 citations · 15 across the 7 of their papers we have counts for
6 papers · 1 filter
Deconstructing Auslander's formulas, I. Fundamental sequences associated with additive functors
Alex Martsinkovsky
For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derive…
The defect, the Malgrange functor, and linear control systems
Alex Martsinkovsky
The notion of defect of a finitely presented functor on a module category is extended to arbitrary additive functors. The new defect and the contravariant Yoneda embedding form a r…
Orders of bounded and strongly unbounded lattice type
Fahimeh Sadat Fotouhi, Alex Martsinkovsky, Shokrollah Salarian
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algeb…
Injective stabilization of additive functors. III. Asymptotic stabilization of the tensor product
Alex Martsinkovsky, Jeremy Russell
The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. The limit of this procedure, called the asymptotic st…
Injective stabilization of additive functors. II. (Co)torsion and the Auslander-Gruson-Jensen functor
Alex Martsinkovsky, Jeremy Russell
The formalism of injective stabilization of additive functors is used to define a new notion of the torsion submodule of a module. It applies to arbitrary modules over arbitrary ri…
Injective stabilization of additive functors. I. Preliminaries
Alex Martsinkovsky, Jeremy Russell
This paper is the first one in a series of three dealing with the concept of injective stabilization of the tensor product and its applications. Its primary goal is to collect know…