On the Subcategories of n-Torsionfree Modules and Related Modules

TL;DR

This paper explores the properties and relationships of n-torsionfree modules over commutative noetherian rings, comparing them with n-syzygy modules and modules satisfying Serre's condition, focusing on subcategory closedness.

Contribution

It provides new insights into the structure and closedness properties of subcategories of n-torsionfree modules, connecting them with n-syzygy modules and Serre's condition (S_n).

Findings

Identifies conditions under which subcategories of n-torsionfree modules are closed.

Establishes relationships between n-torsionfree modules, n-syzygy modules, and Serre's condition.

Provides criteria for closedness properties in the module category.

Abstract

Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre's condition (S_n). We mainly investigate closedness properties of the full subcategories of mod R consisting of those modules.