{"paper":{"title":"Subintegrality, Invertible Modules and Laurent Polynomial Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vivek Sadhu","submitted_at":"2014-04-25T18:37:53Z","abstract_excerpt":"Let $A\\subseteq B$ be a commutative ring extension. Let $\\mathcal I(A, B)$ be the multiplicative group of invertible $A$-submodules of $B$. In this article, we extend a result of Sadhu and Singh by finding a necessary and sufficient condition on an integral birational extension $A\\subseteq B$ of integral domains with $\\dim A\\leq 1$, so that the natural map $\\mathcal I(A,B) \\rightarrow \\mathcal I (A [X, X^{-1}],B [X, X^{-1}])$ is an isomorphism. In the same situation, we show that if $\\dim A\\geq 2$ then the condition is necessary but not sufficient. We also discuss some properties of the cokern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6498","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}