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Torsion elements in effect algebras

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Abstract

We define the torsion element in effect algebras and use it to characterize MV-effect algebra and 0-homogeneous effect algebras in chain-complete effect algebras. As an application, we prove that every element of an orthocomplete homogeneous atomic effect algebra has a unique basic decomposition into a sum of a sharp element and unsharp multiples of atoms. Further, we characterize homogeneity by the set of all sharp elements in orthocomplete atomic effect algebras.

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Acknowledgments

The research was supported by the Natural Science foundation of Shaanxi Province under Grant No. 2007A19 and the foundation of Shaanxi Province Education Ministry under Grant No. 08JK472.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University, Xi’an, 710127, People’s Republic of China

    Wei Ji & Xiao Long Xin

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  1. Wei Ji
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  2. Xiao Long Xin
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Correspondence to Xiao Long Xin.

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Ji, W., Xin, X.L. Torsion elements in effect algebras. Soft Comput 15, 2501–2505 (2011). https://doi.org/10.1007/s00500-011-0712-5

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