15 citations · 15 across the 7 of their papers we have counts for
10 papers
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…
The finite presentation of the stable Hom functors, the Bass torsion, and the cotorsion coradical
Alex Martsinkovsky
We provide necessary and/or sufficient conditions for the stable Hom functors to be finitely presented. When the covariant Hom functor modulo projectives is finitely presented, its…
Cokernels in the stable category of a left hereditary ring
Dali Zangurashvili
It is proved that if a ring is left hereditary, left perfect and right coherent, then the stable category has cokernels. Moreover, we show that the condition for a ring to be left…
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…
The stable category of a left hereditary ring
Alex Martsinkovsky, Dali Zangurashvili
The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category ar…
On direct summands of homological functors on length categories
Alex Martsinkovsky
We show that direct summands of certain additive functors arising as bifunctors with a fixed argument in an abelian category are again of that form whenever the fixed argument has…