44 citations · 110 across the 20 of their papers we have counts for
5 papers · 1 filter
Flat cotorsion modules over Noether algebras
Ryo Kanda, Tsutomu Nakamura
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalizatio…
Finiteness of the number of minimal atoms in Grothendieck categories
Ryo Kanda
For a Grothendieck category having a noetherian generator, we prove that there are only finitely many minimal atoms. This is a noncommutative analogue of the fact that every noethe…
Specialization orders on atom spectra of Grothendieck categories
Ryo Kanda
We introduce systematic methods to construct Grothendieck categories from colored quivers and develop a theory of the specialization orders on the atom spectra of Grothendieck cate…
Extension groups between atoms and objects in locally noetherian Grothendieck category
Ryo Kanda
We define the extension group between an atom and an object in a locally noetherian Grothendieck category as a module over a skew field. We show that the dimension of the i-th exte…
Classifying Serre subcategories via atom spectrum
Ryo Kanda
In this paper, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spec…