Boolean Lifting Property for Residuated Lattices

摘要

In this paper we define the Boolean Lifting Property (BLP) for residuatedlattices to be the property that all Boolean elements can be lifted moduloevery filter, and study residuated lattices with BLP. Boolean algebras, chains,local and hyperarchimedean residuated lattices have BLP. BLP behavesinterestingly in direct products and involutive residuated lattices, and it isclosely related to arithmetic properties involving Boolean elements, nilpotentelements and elements of the radical. When BLP is present, strongrepresentation theorems for semilocal and maximal residuated lattices hold.