LATTICE-ORDERED GROUPS WHOSE LATTICES DETERMINE THEIR ADDITIONS

摘要: In this paper it is shown that several large and important classes of lattice-ordered groups, including the free abelian have their group operations completely determined by underlying lattices, or de- termined up to /-isomorphism. integers Z with usual order <, 1 covers 0. From simple fact, easy see (Z, <) a uniquely transitive chain as defined Ohkuma (24) singular element. Either property enough show that, having chosen 0 be identity Z, addition specified chain. paper, we these properties are sufficiently general pow- erful prove many familiar groups also lattice choice an identity. particular, will Theorem A. Every has unique addition. B. If G archimedean if for any < g e G, there exists element s such g, then