Abstract
In the present paper, we introduce a proper superclass of homogeneous effect algebras. We call this superclass as 0-homogeneous effect algebras. We prove that in every 0-homogeneous effect algebra, the set of all sharp elements forms a subalgebra. Every chain-complete 0-homogeneous effect algebra is homogeneous.
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References
Bennett M, Foulis D (1997) Interval and scale effect algebras. Adv Appl Math 19:200–215
Bush P, Grabowski M, Lahti P (1995) Operational quantum physics. Springer, Berlin
Chang C (1959) Algebraic analysis of many-valued logics. Trans Am Math Soc 88:467–490
Chovanec F and Kôpka F (1997) Boolean D-posets. Tatra Mt Math Publ 10:183–197
Dvurečenskij A, Pulmannová S (2000) New Trends in Quantum Structures. Kluwer, Dordrecht and Ister Science, Bratislava
Foulis D, Bennett M (1994) Effect algebras and unsharp quantum logics. Found Phys 24:1325–1346
Giuntini R, Greuling H (1989) Toward a formal language for unsharp properties. Found Phys 19:931–945
Gudder S (1998) S-dominating effect algebras. Int J Theor Phys 37:915–923
Jenča G (2001) Blocks of homogeneous effect algebras. Bull Aust Math Soc 64:81–98
Jenča G (2007) The block structure of complete lattice ordered effect algebras. J Aust Math Soc 83:181–216
Jenča G, Riečanová Z (1999) On sharp elements in lattice ordered effect algebras. BUSEFAL 80:24–29
Kalmbach G (1983) Orthomodular Lattices. Academic Press, New York
Kôpka F (1992) D-posets of fuzzy sets. Tatra Mt Math Publ 1:83–87
Kôpka F, Chovanec F (1994) D-posets. Math Slovaca 44:21–34
Ludwig G (1983) Foundations of quantum mechanics. Springer, Berlin
Mundici D (1986) Interpretation of AF C*-algebras in Lukasziewicz sentential calculus. J Funct Anal 65:15–53
Riečanová Z (2000) A generalization of blocks for D-lattices and lattice effect algebras. Int J Theor Phys 39:231–237
Acknowledgments
This research is supported by Grants VEGA G-1/3025/06,G-1/0500/09 of MŠ SR, Slovakia and by the Slovak Research and Development Agency under the contracts No. APVT-51-032002, APVV-0071-06.
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Jenča, G. 0-homogeneous effect algebras. Soft Comput 14, 1111–1116 (2010). https://doi.org/10.1007/s00500-009-0505-2
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DOI: https://doi.org/10.1007/s00500-009-0505-2