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Relative annihilators in bounded commutative residuated lattices

Author

Listed:
  • Ariane G. Tallee Kakeu

    (University of Dschang)

  • Blaise B. Koguep Njionou

    (University of Dschang)

  • Celestin Lele

    (University of Dschang)

  • Lutz Strüngmann

    (Mannheim University of Applied Sciences)

Abstract

In this work, we introduce the concept of relative annihilator of a subset of a bounded commutative residuated lattice L with respect to an ideal and investigate related properties. We show that the relative annihilator of an ideal J with respect to an ideal I is the pseudo-complement of J with respect to I within the lattice of all ideals of L. We also study essential ideals, involutory ideals with their properties, and give some characterizations of prime ideals.

Suggested Citation

  • Ariane G. Tallee Kakeu & Blaise B. Koguep Njionou & Celestin Lele & Lutz Strüngmann, 2023. "Relative annihilators in bounded commutative residuated lattices," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 359-374, June.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:2:d:10.1007_s13226-022-00258-1
    DOI: 10.1007/s13226-022-00258-1
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    References listed on IDEAS

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    1. Albert Kadji & Celestin Lele & Jean B. Nganou & Marcel Tonga, 2014. "Folding Theory Applied to Residuated Lattices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-12, June.
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