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Generalized EMV-Effect Algebras

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Abstract

Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

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Acknowledgements

AD is thankful for the support by the grant of the Slovak Research and Development Agency under contract APVV-16-0073 by the grants VEGA No. 2/0069/16 SAV, and GAČR 15-15286S

The authors are very indebted to the anonymous referee for his/her careful reading and suggestions which helped us to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei & A. H. Sharafi

  2. Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia

    A. Dvurečenskij

  3. Department of Algebra Geometry, Palacký University, Olomouc, Czech Republic

    A. Dvurečenskij

Authors
  1. R. A. Borzooei
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  2. A. Dvurečenskij
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  3. A. H. Sharafi
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Correspondence to R. A. Borzooei.

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Borzooei, R.A., Dvurečenskij, A. & Sharafi, A.H. Generalized EMV-Effect Algebras. Int J Theor Phys 57, 2267–2279 (2018). https://doi.org/10.1007/s10773-018-3750-2

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  • DOI: https://doi.org/10.1007/s10773-018-3750-2

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