TL;DR
This paper introduces and explores properties of S-rings of Krull type, including characterizations and the injective dimension of related quotient categories, advancing the understanding of their algebraic structure.
Contribution
It defines S-rings of Krull type, provides their properties and characterizations, and determines the injective dimension of a specific quotient category for independent S-rings of Krull type.
Findings
Characterization of S-rings of Krull type
Properties of these rings
Calculation of injective dimension of quotient categories
Abstract
We define and give some properties and characterizations of S-rings of Krull type. We also determine, in the case of an independent S-ring of Krull type A, the injective dimension of the quotient category Mod(A)/\mathcal{M}_{0}, where \mathcal{M}_{0} is the thick subcategory of the modules with trivial maps into the codivisorial modules.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models