{"paper":{"title":"Split Lie-Rinehart algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Antonio J. Calder\\'on, Elisabete Barreiro, Helena Albuquerque, Jos\\'e M. S\\'anchez","submitted_at":"2017-06-21T19:00:43Z","abstract_excerpt":"We introduce the class of split Lie-Rinehart algebras as the natural extension of the one of split Lie algebras. We show that if $L$ is a tight split Lie-Rinehart algebra over an associative and commutative algebra $A,$ then $L$ and $A$ decompose as the orthogonal direct sums $L = \\bigoplus_{i \\in I}L_i$, $A = \\bigoplus_{j \\in J}A_j$, where any $L_i$ is a nonzero ideal of $L$, any $A_j$ is a nonzero ideal of $A$, and both decompositions satisfy that for any $i \\in I$ there exists a unique $\\tilde{i} \\in J$ such that $A_{\\tilde{i}}L_i \\neq 0$. Furthermore any $L_i$ is a split Lie-Rinehart algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07084","kind":"arxiv","version":1},"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"}