Title of article :
Regularity in residuated lattices
Author/Authors :
Holdon, L.C Faculty of Exact Sciences - Department of Mathematics - University of Craiova, 13, Al. I.Cuza st., Craiova, Romania , Borumand Saeid, A Mahani Mathematical Research center - Shahid Bahonar University of Kerman, Iran
Abstract :
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 lter called special lter and investigate its properties.
Finally, regular lter property in residuated lattices is introduced and is studied in details.
Keywords :
free algebras , directly indecomposable algebra , Boolean element , (Semi) divisible residuated lattice
