Classes of pseudo BL-algebras with right Boolean lifting property

In this paper, we define the right Boolean lifting property (left Boolean lifting property) RBLP (LBLP) for pseudo BL-algebra to be the property that all Boolean elements can be lifted modulo every right filter (left filter) and next we study the behavior of RBLP (LBLP) with respect to direct products of pseudo BL-algebra. We introduce some conditions, which turn out to be a strengthening and a weakling of RBLP (LBLP) respectively and which open new ways of approaching the study of the RBLP (LBLP) in pseudo BL-algebras.