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Relative annihilators in bounded commutative residuated lattices

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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.

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Acknowledgements

The authors would like to thank the anonymous referees for the careful reading and for their valuable comments that have substantially improved this paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Ariane G. Tallee Kakeu, Blaise B. Koguep Njionou & Celestin Lele

  2. Faculty of Computer Science, Mannheim University of Applied Sciences, 68163, Mannheim, Germany

    Lutz Strüngmann

Authors
  1. Ariane G. Tallee Kakeu
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  2. Blaise B. Koguep Njionou
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  3. Celestin Lele
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  4. Lutz Strüngmann
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Corresponding author

Correspondence to Ariane G. Tallee Kakeu.

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Communicated by Bakshi Gurmeet Kaur.

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Tallee Kakeu, A.G., Koguep Njionou, B.B., Lele, C. et al. Relative annihilators in bounded commutative residuated lattices. Indian J Pure Appl Math 54, 359–374 (2023). https://doi.org/10.1007/s13226-022-00258-1

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  • DOI: https://doi.org/10.1007/s13226-022-00258-1

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