Relative annihilators in bounded commutative residuated lattices

Ariane G. Tallee Kakeu (), Blaise B. Koguep Njionou (), Celestin Lele () and Lutz Strüngmann ()
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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

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 359-374

Abstract: 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.

Keywords: Bounded commutative residuated lattice; Ideal; Prime ideal; Relative annihilator; Essential ideal; Involutory ideal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00258-1

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