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Ordinal length and the canonical topology

2013/01/28 by Hans Schoutens, Schoutens, Hans · 1 citation
Computer Science · Mathematics · #13E05 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Topological and Geometric Data Analysis #math.AC #math.LO #msc:13E05

paper · pdf · doi:10.48550/arxiv.1301.6457

arxiv created 2013/01/28 · openalex publication_date 2013/01/28 · arxiv updated 2013/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the classical length function to an ordinal-valued invariant on the class of all finite-dimensional Noetherian modules. We show how to calculate this combinatorial invariant by means of the fundamental cycle of the module, thus linking the lattice of submodules to homological properties of the module. Using this, we define on a module its canonical topology, in which every morphism is continuous.

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