{"paper":{"title":"Algorithms for determination of t-module structures on some extension groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dawid E. K\\k{e}dzierski, Filip G{\\l}och, Piotr Kraso\\'n","submitted_at":"2024-08-15T15:18:42Z","abstract_excerpt":"In \\cite{kk04} the second and third author extended the methods of \\cite{pr} and determined the \\tm module structure on $\\Ext^1(\\Phi,\\Psi )$ where $\\Phi $ and $\\Psi$ were Anderson \\tm modules over $A={\\mathbf F}_q[t]$ of some specific types. This approach involved the concept of biderivation and certain reduction algorithm. In this paper we generalize the results of \\cite{pr} and \\cite{kk04} and present complete algorithm for computation of \\tm module structure on $\\Ext^1(\\Phi,\\Psi )$ for \\tm modules $\\Phi $ and $\\Psi$ such that $\\rk \\Phi > \\rk \\Psi.$ The last condition is not sufficient for o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.08207","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.08207/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}