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Very true operators in effect algebras

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Abstract

We introduce the concept of very true operator on an effect algebra. Although an effect algebra is only partial, we define it in the way which is in accordance with traditional definitions in residuated lattices or basic algebras. This is possible if we require monotonicity as an additional condition. We prove that very true operators on effect algebras can be characterized by means of certain subsets which are conditionally complete.

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Acknowledgments

The work of the first author is supported by the project Algebraic Methods in Quantum Structures, No. CZ.1.07/2.3.00/20.0051.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Ivan Chajda

  2. Department of Computer Science, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Miroslav Kolařík

Authors
  1. Ivan Chajda
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  2. Miroslav Kolařík
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Correspondence to Ivan Chajda.

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Chajda, I., Kolařík, M. Very true operators in effect algebras. Soft Comput 16, 1213–1218 (2012). https://doi.org/10.1007/s00500-012-0807-7

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  • DOI: https://doi.org/10.1007/s00500-012-0807-7

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