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Shinnosuke Kosaka

Publications and source records attributed to Shinnosuke Kosaka.

4 recordsLinked to original sources
arXiv2026

Torsion pairs in subcategories of modules over a commutative ring

Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. Let $\Delta$ be a subset of $\operatorname{Spec} R$, and let $\operatorname{Ass}^{-1}\Delta$ stand for the full subcategory of $\operatorname{mod} R$ consisting of finitely generated $R$-modules whose associated prime ideals belong to $\Delta$. In this paper, we consider classifying torsion pairs in $\operatorname{Ass}^{-1}\Delta$ and some other full subcategories of $\operatorname{mod} R$.

math.AC↗
arXiv2025

Characterizing Regular Local Rings via Analogues of (*)-properties

Let $R$ be a commutative noetherian local ring. As analogues of $(*)$-properties introduced by Ghosh, Gupta, and Puthenpurakal, we introduce and study $(\mathrm{A})$-properties, $(\mathrm{B})$-properties, and $(\mathrm{C})$-relations. Using these three notions, we establish a criterion for a local ring to be regular. This recovers and refines the main result of Ghosh, Gupta, and Puthenpurakal and has further applications.

math.AC↗
arXiv2025

Criteria for finite injective dimension of modules over a local ring

Let $R$ be a commutative Noetherian local ring. We prove that the finiteness of the injective dimension of a finitely generated $R$-module $C$ is determined by the existence of a Cohen--Macaulay module $M$ that satisfies an inequality concerning multiplicity and type, together with the vanishing of finitely many Ext modules. As applications, we recover a result of Rahmani and Taherizadeh and provide sufficient conditions for a finitely generated $R$-module to have finite injective dimension.

math.AC↗