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α-Ideals in Bounded Commutative Residuated Lattices

Author

Listed:
  • Ariane G. Tallee Kakeu

    (Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon)

  • Lutz Strüngmann

    (Faculty of Computer Science, Mannheim University of Applied Sciences, Mannheim 68163, Germany)

  • Blaise B. Koguep Njionou

    (Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon)

  • Celestin Lele

    (Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, West Region, Cameroon)

Abstract

This study aims to introduce the concept of α-ideal in bounded commutative residuated lattices and establish some related properties. In this paper, we show that the set of α-ideals of a bounded commutative residuated lattice is a Heyting algebra, and an algebraic lattice. Moreover, we state the prime α-ideal theorem, and describe relations between α-ideals and some types of ideals of a bounded commutative residuated lattice. Finally, we discuss correspondences between α-ideals and α-filters of a bounded commutative residuated lattice.

Suggested Citation

  • Ariane G. Tallee Kakeu & Lutz Strüngmann & Blaise B. Koguep Njionou & Celestin Lele, 2023. "α-Ideals in Bounded Commutative Residuated Lattices," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 611-630, November.
    • Handle: RePEc:wsi:nmncxx:v:19:y:2023:i:03:n:s1793005723500254
    DOI: 10.1142/S1793005723500254
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