Affiliation:
1. Departamento de Matemática Facultad de Ciencias Exactas Universidad Nacional del Centro de la Provincia de Buenos Aires, and Conicet Argentina
2. Departamento de Matemática Facultad de Ciencias Exactas Universidad Nacional de La Plata, and Conicet Argentina
Abstract
AbstractA subresiduated lattice is a pair , where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set , which is denoted by . This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where . The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by , whose members satisfy the equation . Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every .
Funder
Consejo Nacional de Investigaciones Científicas y Técnicas
Universidad Nacional de La Plata
Agencia Nacional de Promoción Científica y Tecnológica
Reference11 articles.
1. Some results for implicational calculi
2. On Hilbert algebras generated by the order
3. Sub-Hilbert Lattices
4. J. L.Castiglioni V.Fernández H. F.Mallea andH. J.San Martín On subreducts of subresiduated lattices and logic arXiv:2211.02963(2022).