On some completeness properties for lattice ordered groups
Ján Jakubík · Czechoslovak Mathematical Journal · 1995
Buskes [2] investigated a series of completeness properties for an archimedean Riesz space E. Each of these properties can be applied also in a more general setting, i.e., for the case when E is a lattice ordered group.If a is one of the properties under consideration, then we denote by Ga the class of all lattice ordered groups G which have the property a.The notion of radical class of lattice ordered groups was introduced in [8]; cf. also [4], [5], [12], [13], [16]. The relations between this notion and the classes Ga will be dealt with in the present paper.We are mainly interested in the question whether Ga (or some reasonably large subclass of Ga) is a radical class.This question is related to the problem of existence of a-kernels.For some properties defined by means of sequences similar considerations were established in [10] and [11].