2014•Mathematica SlovacaOpen access

On a type of distributivity of lattice ordered groups

Ján Jakubík

Abstract

Abstract Let m be an infinite cardinal. Inspired by a result of Sikorski on m-representability of Boolean algebras, we introduce the notion of r m-distributive lattice ordered group. We prove that the collection of all such lattice ordered groups is a radical class. Using the mentioned notion, we define and investigate a homogeneity condition for lattice ordered groups.

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Key concepts: Distributivity, Mathematics, Congruence lattice problem, Lattice (music), Distributive lattice, Distributive property, Map of lattices, Combinatorics