A Curious Characterisation of Dedekind Domains
Robert Szafarczyk
TL;DR
This paper characterizes Dedekind domains among broader classes of rings using a novel property related to module homomorphisms, employing homological algebra techniques.
Contribution
It introduces a new characterization of Dedekind domains that applies beyond Noetherian cases, expanding understanding of their algebraic structure.
Findings
Dedekind domains characterized by module homomorphism properties
Homological algebra used to prove the characterization
Applicable to non-Noetherian domains
Abstract
We characterise Dedekind rings among not necessarily Noetherian domains by a property of their module homomorphisms. Our proof relies on a homological algebra argument.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications