Embedding of semilattices into distributive lattices
Jiří Fábera, Teo Sturm · Czechoslovak Mathematical Journal · 1979
Part I of the present paper contains the definition of the r-hull of a meet-semilattice ^ (it is an r-distributive lattice, free generated by ^ and having some natural properties with respect to 5^) and some elementary consequences of this definition. Part II contains a construction of the r-hull. Part III contains an other construction of the r-hull (which is similar to the McNeille completization).Tliis purely algebraic paper is motivated by measure theory: the theory developed so far enables an abstract characterization of semi-rings of sets [2].On such abstract semi-rings "additive" functions are considered with values from suitable algebraic structures and their additive extensions are investigated.The authors wish to thank to Dr. JIRI ADAMEK for helpful discussions and suggestion which made possible to simplificate some of the constructions in part II.They wish to thank also to Dr. JANA RYSLINKOVÂ for her translation and useful remarks.