{
  "id": "0812.2502",
  "version": "v2",
  "published": "2008-12-12T23:09:02.000Z",
  "updated": "2009-03-30T03:03:05.000Z",
  "title": "Not each sequential effect algebra is sharply dominating",
  "authors": [
    "Shen Jun",
    "Wu Junde"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "quant-ph"
  ],
  "abstract": "Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$. $E$ is said to be sharply dominating if for each $a\\in E$ there exists a smallest element $\\widehat{a}\\in E_s$ such that $a\\leq \\widehat{a}$. In 2002, Professors Gudder and Greechie proved that each $\\sigma$-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-30T03:03:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "professors gudder",
      "open problems",
      "international journal",
      "3th problem",
      "professor gudder"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2502J"
    }
  }
}