{"paper":{"title":"Remarks on the sequential effect algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.LO","math.MP","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Shen Jun, Wu Junde","submitted_at":"2009-03-30T02:55:59Z","abstract_excerpt":"In this paper, first, we answer affirmatively an open problem which was presented in 2005 by professor Gudder on the sub-sequential effect algebras. That is, we prove that if $(E,0,1, \\oplus, \\circ)$ is a sequential effect algebra and $A$ is a commutative subset of $E$, then the sub-sequential effect algebra $\\bar{A}$ generated by $A$ is also commutative. Next, we also study the following uniqueness problem: If $na=nb=c$ for some positive integer $n\\geq 2$, then under what conditions $a=b$ hold? We prove that if $c$ is a sharp element of $E$ and $a|b$, then $a=b$. We give also two examples to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5116","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"}