Contravariantly infinite resolving subcategories

Abstract

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