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Implicative hyper K-algebras

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Abstract

In this note we first define the notions of (weak, strong) implicative hyper K-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we obtain some relations between these notions and (weak) implicative hyper K-ideals. Finally, we study the implicative hyper K-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper K-algebras and (weak, strong) implicative hyper K-algebras under a simple condition.

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Authors and Affiliations

  1. Dept. of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    M. M. Zahedi

  2. Dept. of Mathematics, Islamic Azad University, Kerman, Iran

    A. Borumand Saeid

  3. Dept. of Mathematics, Sistan and Baluchestan University, Zahedan, Iran

    R. A. Borzooei

Authors
  1. M. M. Zahedi
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  2. A. Borumand Saeid
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  3. R. A. Borzooei
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Zahedi, M.M., Saeid, A.B. & Borzooei, R.A. Implicative hyper K-algebras. Czech Math J 55, 439–453 (2005). https://doi.org/10.1007/s10587-005-0034-9

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  • DOI: https://doi.org/10.1007/s10587-005-0034-9

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