Modules with fusion and implication based over distributive lattices: Representation and duality-Reference-Cited by-同舟云学术

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

Published:2022-03-28 Issue:2 Volume:72 Page:301-318
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Calomino Ismael¹,Zuluaga Botero William J.²³

Affiliation:

1. CIC and Departamento de Matemática Facultad de Ciencias Exactas , Universidad Nacional del Centro , Tandil , Argentina

2. Laboratoire J. A. Dieudonné , Université Côte ďAzur , Nice , France

3. Departamento de Matemática Facultad de Ciencias Exactas , Universidad Nacional del Centro , Tandil , Argentina

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0020/pdf

Reference19 articles.

1. Balbes, R.—Dwinger, P.: Distributive Lattices, University of Missouri Press, 1974.

2. Blackburn, P.—de Rijke, M.—Venema, Y.: Modal Logic, Cambridge University Press, 2001.

3. Burmeister, P.: Lecture Notes on Universal Algebra, Many-Sorted Partial Algebras, manuscript available via internet, 2002.

4. Cabrer, L.—Celani, S.: Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras, Cent. Eur. J. Math. 4 (2006), 600–623.

5. Celani, S.: Ditributive lattices with fusion and implication, Southeast Asian Bull. Math. 28 (2004), 999–1010.