On abelian pseudo lattice ordered groups
J. Roger Teller · Pacific Journal of Mathematics · 1968
Throughout this paper po-group will mean partially ordered abelian group.is a value of #} and ^^*(g)= f\^st(g).Two positive elements a y beG are pseudo disjoint (p-dis joint) if α€^C*(6) and &e^^*(α), and G is a pseudo-lattice ordered group (pl-group) if each g e G can be written g = a -b where a and b are ^-disjoint.The main result of § 2 shows that every pl-group G is a Riesz group.That is, G is semiclosed ing ^ 0 implies g ^ 0 for all #eG and all positive integers n), and G satisfies the Riesz interpolation property; if, whenever x u , # TO , y u --,y n are elements of G and #» ^ ?/i for 1 ^ ΐ ^ m, 1 ^ i ^ n, then there is an element 26G such that Xi ^ z S yj.