Regularity in residuated lattices

Document Type : Research Paper


1 Faculty of Exact Sciences, Department of Mathematics, University of Craiova, 13, Al. I.Cuza st., 200585, Craiova, Romania and International Theoretical High School of Informatics Bucharest, 648, Colentina st., 021187 Bucharest, Romania

2 Mahani Mathematical Research center, Shahid Bahonar University of Kerman, Iran, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran


In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in residuated lattice a new type of filter called special filter and investigate its properties. Finally, regular filter property in residuated lattices is introduced and is studied in details.