{"paper":{"title":"On the polynomial identities of the algebra $M_{11}(E)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Plamen Koshlukov, Thiago Castilho de Mello","submitted_at":"2012-08-10T14:22:30Z","abstract_excerpt":"Verbally prime algebras are important in PI theory. They were described by Kemer over a field $K$ of characteristic zero: 0 and $K<T>$ (the trivial ones), $M_n(K)$, $M_n(E)$, $M_{ab}(E)$. Here $K<T>$ is the free associative algebra of infinite rank, with free generators $T$, $E$ denotes the infinite dimensional Grassmann algebra over $K$, $M_n(K)$ and $M_n(E)$ are the $n\\times n$ matrices over $K$ and over $E$, respectively. The algebras $M_{ab}(E)$ are subalgebras of $M_{a+b}(E)$, see their definition below. The generic (also called relatively free) algebras of these algebras have been studie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2185","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"}