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21 papers
On the homological conjectures for Artin algebras
Haruhisa Enomoto, Rene Marczinzik
We prove that the Auslander--Reiten conjecture, the generalised Nakayama conjecture, the Nakayama conjecture, and each of the two Tachikawa conjectures are globally equivalent for…
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…
The Cartan determinant conjecture for representation-finite algebras
Haruhisa Enomoto
Let be a finite-dimensional representation-finite algebra over an algebraically closed field , and let be a finite-dimensional -module such that $\operatorname{End}_A…
An equidistribution conjecture for quotient-closed and submodule-closed subcategories
Haruhisa Enomoto
We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules. We propose the quotient--submodule equidistribution con…
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…