IE-closed subcategories of commutative rings are torsion-free classes
I proved the title
Papers
You can also find my papers (preprints) on my arXiv page.
Preprints
Maximal self-orthogonal modules and a new generalization of tilting modules
Study maximal self-orthogonal modules, a new generalization of tilting modules = projectively Wakamatsu tilting modules, and Wakamatsu tilting modules
Grothendieck monoids of extriangulated categories
Study the Grothendieck monoid of an extriangulated category.
Publications
Image-extension-closed subcategories of module categories of hereditary algebras
Study subcategories of a module category closed under images and extensions.
From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
Compute the posets of wide subcats and ICE-closed subcats from the lattice of torsion classes
Intervals of s-torsion pairs in extriangulated categories with negative first extensions
Unify bijections of the form “Interval poset of torsion pairs is isomorphic to the poset of torsion pairs in another subcategory” in the framework of extriangulated categories.
Rigid modules and ICE-closed subcategories in quiver representations
Established a bijection between Image-Cokernel-Extension-closed (ICE-closed) subcats in mod kQ and rigid kQ-modules
The Jordan-Hölder property and Grothendieck monoids of exact categories
I consider when an exact category satisfies the Jordan-Hölder property, (JHP).
Monobrick, a uniform approach to torsion-free classes and wide subcategories
Motivated by the study of simple objects of exact categories, I proposed the notion of monobricks, which enables us to study wide subcategories and torsion-free classes simultaneously.
Schur’s lemma for exact categories implies abelian
I proved the title.
ICE-closed subcategories and wide τ-tilting modules
Study Image-Cokernel-Extension closed subcategories of module categories using the poset of torsion classes and τ-tilting theory.
Classifying substructures of extriangulated categories via Serre subcategories
Classified a possible extriangulated substructures on a given extriangulated category using functor category
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
For torsion-free classes over preprojective algebras and path algebras of Dynkin type, I classify simple objects using the root system.
Relations for Grothendieck groups and representation-finiteness
Rep-fin v.s. “AR seq generate relations for K_0” in exact categories.
Classifications of exact structures and Cohen-Macaulay-finite algebras
I classify possible exact structures on a given additive category by using functor category, and give applications to CM-finite Iwanaga-Gorenstein algebras.
Classifying exact categories via Wakamatsu tilting
Study the Morita type theorem for exact categories. The Ext-perpendicular category of cotilting modules are precisely exact category with progen & inj cogen & higher kernels.
Published proceedings
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H. Enomoto, The Jordan-Hölder property, Grothendieck monoids and Bruhat inversions, Ring Theory 2019, Proceedings of the Eighth China–Japan–Korea International Symposium on Ring Theory (2021), 103–-112.
This is a survey article of this JHP paper. Link: journal