6 papers
Classifying localizing subcategories of a locally coherent category
Reza Sazeedeh
Let $\cA$ be a locally coherent Grothendieck category, $\fp\cA$ be the full subcategory of $\cA$ consisting of finitely presented objects and $\ASpec\cA$ be the atom spectrum of $\…
Classifying subcategories of a Grothendieck category via its spectral category
Reza Sazeedeh
Let be a Grothendieck category. In this paper we classify subcategories of via a support notion defined by Krause \cite{Kr2024} based on the spectral ca…
A new dimension for Grothendieck categories via the atom spectrum
Negar Alipour, Reza Sazeedeh
In this paper, we define a new dimension for objects in a Grothendieck category . We show that it serves as a lower bound for Gabriel-Krull dimension and under certain…
On the category of cofinite complexes and modules
Reza Sazeedeh
Let be a commutative noetherian ring, let be an ideal of . In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes…
Gorenstein injective filtrations over rings with dualizing complexes
Reza Sazeedeh
Let be a commutative noetherian ring. Enochs and Huang [EH] proved that over a Gorenstein ring of Krull dimension , every Gorenstein injective module admits a finite filtrat…
Spectrum of an abelian category via premonoform objects
Reza Sazeedeh
Let $\cA$ be an abelian category. In this paper, we study ${\rm (n)PSpec}\cA$, a topological space formed by equivalence classes derived from an equivalence relation on (noetherian…