Not each sequential effect algebra is sharply dominating

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 ∈ E there exists a smallest element a ˆ ∈ E s such that a ⩽ a ˆ . In 2002, Professors Gudder and Greechie proved that each σ-sequential effect algebra is sharply dominating. In...

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Bibliographic Details
Published inPhysics letters. A Vol. 373; no. 20; pp. 1708 - 1712
Main Authors Shen, Jun, Wu, Junde
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2009
Subjects
Sequential effect algebra
Sharp element
Sharply dominating
Sequential effect algebra
Sharp element
Sharply dominating
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Summary: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 ∈ E there exists a smallest element a ˆ ∈ E s such that a ⩽ a ˆ . In 2002, Professors Gudder and Greechie proved that each σ-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in [S. Gudder, Int. J. Theory Phys. 44 (2005) 2219], the 3rd problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2009.02.073