On Divisor Topology of Modules over Domains
\"Unsal Tekir, U\u{g}ur Yi\u{g}it, Mesut Bu\u{g}day, Suat Ko\c{c}

TL;DR
This paper introduces a divisor topology on the set of nonzero nongenerators of a module over a domain, extending existing topologies, and explores its properties and applications to various classes of modules.
Contribution
It constructs and analyzes a new divisor topology on modules, extending the divisor topology from domains, and characterizes module classes via this topology.
Findings
D(M) satisfies various separation axioms and countability properties.
D(M) is a Baire space for factorial modules.
Characterization of modules like uniserial, simple, and finitely cogenerated via D(M).
Abstract
Let be a module over a domain and be the set of all nonzero nongenerators of Consider following equivalence relation on as follows: for every if and only if Let be the set of all equivalence classes of with respect to . In this paper, we construct a topology on which is called divisor topology of and denoted by Actually, is extension of the divisor topology over domains in the sense of Yi\u{g}it and Koc to modules. We investigate separation axioms for every first and second countability, connectivity, compactness, nested property, and Noetherian property on . Also, we characterize some important classes of modules such as uniserial modules, simple modules, vector spaces, and finitely…
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Taxonomy
TopicsRings, Modules, and Algebras · Manufacturing Process and Optimization · Resource-Constrained Project Scheduling
