Some examples of BL-algebras using commutative rings

Abstract

The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and we give summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equiped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings are established. Also, we give examples of finite BL-rings for which their lattice of ideals is not an MV-algebra and using these rings we construct BL-algebras with $2^r+1$ elements, $r\ge 2,$ and \ all BL-chains with $k$ elements, $k\ge 4.$