REPRESENTATION OF A UNITAL GROUP HAVING A FINITE UNIT INTERVAL
David J. Foulis · Demonstratio Mathematica · 2003
Let G ^ {0} be a unital group with a finite unit interval and with rank r.Then r is a positive integer and G can be realized as TI x K, where K is a finite abelian group, in such a way that (z, k) € G + => z G (Z + ) r .The state space f2(G) of G is a polytope and the extreme points of f2(G) are Q-valued states.The positive cone G+ satisfies the descending chain condition, and if G is torsion free, then G carries a separating set of Q-valued states.