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Soft Computing
Published in: Soft Computing 11/2012

01-11-2012 | Original Paper

E-perfect effect algebras

Authors: Yongjian Xie, Yongming Li, Aili Yang

Published in: Soft Computing | Issue 11/2012

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Abstract

The definition of E-perfect effect algebras is introduced, and their structure is studied. We study the lexicographical product of an effect algebra with any upwards directed partially ordered Abelian group, and we show that every E-perfect effect algebra is isomorphic with such a kind of the lexicographical product.
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Literature
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Chevalier G, Pulmannová S (2000) Some ideal lattices in partial abelian monoids and effect algebras. Order 17:75–92
Dvurečenskij A (2007) Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups. J Aust Math Soc 82:183–207
Dvurečenskij A, Pulmannová S (2000) New trends in quantum structures. Kluwer Academic Publishers, Dordrecht
Dvurečenskij A, Vetterlein T (2001) Pseudoeffect algebas I. Basic properties. Int J Theor Phys 40:685–701
Dvurečenskij A, Vetterlein T (2001) Pseudoeffect algebras. II. Group representation. Int J Theor Phys 40:703–726
Dvurečenskij A, Vetterlein T (2002) Algebras in the positive cone of po-groups. Order 19:127–146
Foulis DJ, Bennett MK (1994) Effect algebras and unsharp quantum logics. Found Phys 24:1325–1346
Goodearl KR (1986) Partially ordered Abelian groups with interpolation. American Mathematical Society Providence, Rhode Island
Kôpka F, Chovanec F (1994) D-posets. Math Slov 44:21–34
Kalmbach G (1983) Orthomodular lattices. London Mathematical Society, Monographs, vol 18. Academic Press, London
Ravindran K (1996) On a structure theory of effect algebras, Ph.D. thesis, Kansas Satae University, Manhatan, pp 1–54
Vetterlein T (2003) Existence of states on pseudoeffect algebras. Int J Theor Phys 42:673–695
Yongming L (2008) Structures of scale generalized effect algebras and scale effect algebras. Acta Math Sin 51:863–876 (in Chinese)
Metadata
Title
E-perfect effect algebras
Authors
Yongjian Xie
Yongming Li
Aili Yang
Publication date
01-11-2012
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 11/2012
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-012-0865-x

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