{"paper":{"title":"Primeness property for central polynomials of verbally prime P.I. algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Diogo Diniz Pereira da Silva e Silva","submitted_at":"2014-07-04T19:54:57Z","abstract_excerpt":"Let $f$ and $g$ be two noncommutative polynomials in disjoint sets of variables. An algebra $A$ is verbally prime if whenever $f\\cdot g$ is an identity for $A$ then either $f$ or $g$ is also an identity. As an analogue of this property Regev proved that the verbally prime algebra $M_k(F)$ of $k\\times k$ matrices over an infinite field $F$ has the following primeness property for central polynomials: whenever the product $f\\cdot g$ is a central polynomial for $M_k(F)$ then both $f$ and $g$ are central polynomials. In this paper we prove that over a field of characteristic zero Regev' s result h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1311","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"}