{"paper":{"title":"Extending structures, Galois groups and supersolvable associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2013-05-26T12:55:52Z","abstract_excerpt":"Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension $\\mathfrak{c}$, two non-abelian cohomological type objects are explicitly constructed: ${\\mathcal A}{\\mathcal H}^{2}_{A} \\, (V, \\, A)$ will classify all such algebras up to an isomorphism that stabilizes $A$ while ${\\mathcal A}{\\mathcal H}^{2} \\, (V, \\, A)$ provides the classification from H\\\"{o}lder's extension problem viewpoint. A new product, called the unified pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6022","kind":"arxiv","version":6},"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"}