On coverings in the lattice of all group topologies of arbitrary Abelian groups.
We denote by the class of all abelian lattice ordered groups such that each disjoint subset of is finite. In this paper we prove that if , then the cut completion of coincides with the Dedekind completion of .
A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.
This paper deals with a question concerning -ideals of -groups which was proposed by V. M. Kopytov and Z. J. Dimitrov. We shall also investigate a class of -groups which is in a certain sense near to the class of all lattice ordered groups.