2022/02/25 by Jani Jokela, Jokela, Jani
Computer Science · Decision Sciences · #06F20 #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2202.12651
openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the structure theory of mixed lattice vector spaces, which can be viewed as a generalization of the theory of Riesz spaces. More specifically, we study the properties of ideals and bands in mixed lattice spaces, and the related idea of representing a mixed lattice space as a direct sum of disjoint bands. Under certain conditions, these decompositions can also be given in terms of order projections.