On values in relatively normal lattices Original Research Article

In [8, 11, 12] the class IRN was introduced in order to obtain the lattice-theoretic analogues of some results of Conrad (see e.g. [4]). The aim of these paper is to provide other useful constructions in the study of the structure of relatively normal lattices. The introduced notions and results are purely lattice-theoretic extensions of notions and results for lattice-ordered groups [2, 4, 5]. In the second section, the notion of plenary set of a member of the class IRN is introduced and the characterization of maximal plenary sets is given, extending a well-known theorem in l-groups. In the third section with any lattice in IRN is associated a tree and we investigate how the properties of this tree are reflected in the structure of the lattice. For the case of l-groups, one gets some of Conradʹs results in [5].