{"paper":{"title":"On Indecomposable triples associated with nilpotent operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ahmed El Khantach, El Hassan Zerouali","submitted_at":"2019-06-23T00:21:27Z","abstract_excerpt":"We consider in this paper the family of triples $(V, T, U),$ where $ V$ is a finite dimensional space, $T $ is a nilpotent linear operator on $V$ and $U $ is an invariant subspace of $T$. Denote $[U]= ker(T_{|U})$, and $n_U= dim([U] )$. Our main goal is to investigate possible classification of indecomposable triples. The obtained classification depends on the order of nilpotency $p$, on $n_U$ and on $n_V$. Complete classifications are given for arbitrary $p$, when $n_U=1$, and when $n_U=2$ and $n_V \\le 3$. The case $ p \\le 5$, treated in \\cite{ring} is recaptured by using constructive proofs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09523","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"}