Contravariantly infinite resolving subcategories

TL;DR

This paper investigates contravariantly infinite subcategories within finitely generated modules over local complete intersection rings, providing criteria for their identification and expanding understanding of module approximation properties.

Contribution

It introduces criteria for contravariant infiniteness of subcategories in the context of local complete intersection rings, a novel exploration in module approximation theory.

Findings

Criteria established for contravariant infiniteness

Application to local complete intersection rings

Enhanced understanding of module approximation

Abstract

Let $R$ be a commutative Noetherian ring. Denote by $\textrm{mod}R$ the category of finitely generated $R$-modules. In this paper, a contravariantly infinite subcategory of $\textrm{mod}R$ is defined as a full subcategory $\mathscr{X}$ of $\textrm{mod}R$ such that no module outside $\mathscr{X}$ admits a right $\mathscr{X}$-approximation. This paper provides several criteria for contravariant infiniteness in the case where $R$ is a local complete intersection.