The Jordan-Hölder property and Grothendieck monoids of exact categories

DOI10.1016/j.aim.2021.108167OpenAlexW2967670826MaRDI QIDQ2071641

Haruhisa Enomoto

Publication date: 28 January 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.05446

zbMATH Keywords

exact categoryBruhat inversionGrothendieck monoidJordan-Hölder property

Mathematics Subject Classification ID

Representations of quivers and partially ordered sets (16G20) Representations of associative Artinian rings (16G10) Abelian categories, Grothendieck categories (18E10)

Related Items (3)

Composition series of arbitrary cardinality in modular lattices and abelian categories ⋮ Uniqueness of uniform decompositions in exact categories ⋮ Schur's lemma for exact categories implies abelian

Cites Work

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• Monoids of modules and arithmetic of direct-sum decompositions.
• Tilting modules of finite projective dimension
• Direct sum cancellation of Noetherian modules
• Classifications of exact structures and Cohen-Macaulay-finite algebras
• Applications of contravariantly finite subcategories
• Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
• Intersections, sums, and the Jordan-Hölder property for exact categories
• Reduction of exact structures
• Classifying exact categories via Wakamatsu tilting
• Exact categories
• *-MODULES, TILTING, AND ALMOST ABELIAN CATEGORIES
• MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS
• Preprojective algebras and c -sortable words
• Combinatorics of Coxeter Groups
• Clusters, Coxeter-sortable elements and noncrossing partitions
• Polytopes, Rings, and K-Theory
• Noncrossing partitions and representations of quivers
• Higher algebraic K-theory: I
• The Extensional Structure of Commutative Noetherian Rings
• The relationship between homological properties and representation theoretic realization of artin algebras
• Semibricks
• Coxeter groups and quiver representations
• Torsion classes, wide subcategories and localisations
• -tilting theory
• A counterexample to Raikov's conjecture
• Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
• Primitively generated Hall algebras.

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