English

Modules with fusion and implication based over distributive lattices: Representation and Duality

Logic 2020-07-30 v1

Abstract

In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and subdirectly irreducible FIDL-modules. We give a bi-sorted Priestley-like duality for FIDL-modules and moreover, as an application of such a duality, we provide a topological bi-spaced description of the FIDL-congruences. This result will allows us to characterize the simple and subdirectly irreducible FIDL-modules.

Keywords

Cite

@article{arxiv.2007.14500,
  title  = {Modules with fusion and implication based over distributive lattices: Representation and Duality},
  author = {Ismael Calomino and William J. Zuluaga Botero},
  journal= {arXiv preprint arXiv:2007.14500},
  year   = {2020}
}

Comments

17 pages

R2 v1 2026-06-23T17:28:43.605Z