2013/09/25 by Hans Schoutens, Schoutens, Hans
Computer Science · Mathematics · #13E05 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AC #msc:13E05
paper · pdf · doi:10.48550/arxiv.1309.6694
This is an incorporation of the previous ArXiv preprints arXiv:1301.6457 and arXiv:1210.3855
arxiv created 2013/09/25 · openalex publication_date 2013/09/25 · arxiv updated 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. 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 equip each module with its canonical topology.