## 10 Citations

### Exact structures and degeneration of Hall algebras

- MathematicsAdvances in Mathematics
- 2022

### Associahedra for finite type cluster algebras and minimal relations between $\mathbf{g}$-vectors

- Mathematics
- 2019

We show that the mesh mutations are the minimal relations among the $\mathbf{g}$-vectors with respect to any initial seed in any finite type cluster algebra. We then use this algebraic result to…

### Relations for Grothendieck groups of n-cluster tilting subcategories

- MathematicsJournal of Algebra
- 2021

### On the lattice of weakly exact structures

- Mathematics
- 2020

The study of exact structures on an additive category $\mathcal{A}$ is closely related to the study of closed additive sub-bifunctors of the maximal extension bifunctor $\mbox{Ext}^1$ on…

### Auslander–Reiten Triangles and Grothendieck Groups of Triangulated Categories

- MathematicsAlgebras and Representation Theory
- 2021

We prove that if the Auslander–Reiten triangles generate the relations for the Grothendieck group of a Hom-finite Krull–Schmidt triangulated category with a (co)generator, then the category has only…

### Exact subcategories, subfunctors of $\operatorname{Ext}$, and some applications

- Mathematics
- 2022

. Let ( A , E ) be an exact category. We establish basic results that allow one to identify sub(bi)functors of Ext E ( − , − ) using additivity of numerical functions and restriction to…

### Auslander's defects over extriangulated categories: An application for the general heart construction

- MathematicsJournal of the Mathematical Society of Japan
- 2021

The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization of exact categories and triangulated categories. Our first aim is to provide an extension…

## References

SHOWING 1-10 OF 28 REFERENCES

### Relations for Grothendieck groups of Artin algebras

- Mathematics
- 1984

M. C. R. Butler has shown that if A is an artin algebra of finite representation type, then the almost split sequences generate the relations for the Grothendieck group of A. This paper is primarily…

### Classifications of exact structures and Cohen–Macaulay-finite algebras

- MathematicsAdvances in Mathematics
- 2018

### The grothendieck group of the category of modules of finite projective dimension over certain weakly triangular algebras

- Mathematics
- 2000

In this paper we study the category of finitely generated modules of finite projective dimension over a class of weakly triangular algebras, which includes the algebras whose idempotent ideals have…

### Relations for Grothendieck groups of Gorenstein rings

- Mathematics
- 2016

We consider the converse of the Butler, Auslander-Reiten's Theorem which is on the relations for Grothendieck groups. We show that a Gorenstein ring is of finite representation type if the…

### The Homological Theory of Maximal Cohen-Macaulay Approximations

- Mathematics
- 1989

Soclete Mathematlque de FranceMemoire n° 38, 1989, p.5-37.THE HOMOLOGICAL THEORYOFMAXIMAL COHEN-MACAULAY APPROXIMATIONSbyMaurice Auslander (Brandeis) and Ragnar-Olaf Buchweitz (Toronto)Summary. Let R…

### MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS

- Mathematics
- 2001

This paper deals with standardly stratified algebras, a generalization of quasihereditary algebras. As for quasihereditary algebras we show that there is a tilting module naturally associated with…

### $n$-quasi-abelian categories vs $n$-tilting torsion pairs

- MathematicsDocumenta Mathematica
- 2021

Rump and successively Bondal and Van den Bergh provide an equivalence between the notion of quasi-abelian category studied by Schneiders and that of tilting torsion pair on an abelian category. Any…