Year: 2006
Type: preprint
Abstract: Let $R$ be a commutative ring. A full additive subcategory $\C$ of $R$-modules is triangulated if whenever two terms of a short exact sequence belong to $\C$, then so does the third term. In this note we give a classification of triangulated subcategories of finitely generated modules over a principal ideal domain. As a corollary we show that in the category of finitely generated modules over a PID, thick subcategories (triangulated subcategories closed under direct summands), wide subcategories (abelian subcategories closed under extensions) and Serre subcategories (wide subcategories closed under kernels) coincide and correspond to specialisation closed subsets of $\Spec(R)$.
Source: arXiv (Cornell University)
Author: Chebolu, Sunil K.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1788458433