5 papers
Finiteness and growth of brick chain filtrations
Haruhisa Enomoto
We study Ringel's brick chain filtrations over finite-dimensional algebras: filtrations whose factors are filtered by copies of individual bricks, ordered so that morphisms from ea…
A counterexample to the periodicity conjecture for finite-dimensional algebras
Haruhisa Enomoto
The periodicity conjecture asks whether a finite-dimensional algebra is periodic whenever all its simple modules are periodic. We construct a -dimensional counterexample whose…
IE-closed subcategories of commutative rings are torsion-free classes
Haruhisa Enomoto
Let C be a subcategory of the category of finitely generated R-modules over a commutative noetheian ring R. We prove that, if C is closed under images and extensions (which we call…
Image-extension-closed subcategories of module categories of hereditary algebras
Haruhisa Enomoto, Arashi Sakai
We study IE-closed subcategories of a module category, subcategories which are closed under taking Images and Extensions. We investigate the relation between IE-closed subcategorie…
Grothendieck monoids of extriangulated categories
Haruhisa Enomoto, Shunya Saito
We study the Grothendieck monoid (a monoid version of the Grothendieck group) of an extriangulated category, and give some results which are new even for abelian categories. First,…