Solid generators in module categories and applications

Abstract

– Let 𝑅 be a commutative noetherian ring. Denote by mod 𝑅 the category of finitely generated 𝑅 -modules. In the present paper, we introduce the notion of solid subcategories of mod 𝑅 and investigate it. The main result of this paper not only recovers results of Schoutens, Krause and Stevenson, and Takahashi on thick subcategories, but also unifies and extends them to solid subcategories. Moreover, it provides some contributions to the study of the question asking when a thick subcategory is Serre.