Abstract. One of the central results of the early theory of lattice ordered groups is a theorem due to Ján Jakubik, telling that a maximal convex chain containing the identity element is a direct factor. In this paper it is shown --- along the lines of Bigard--Keimel--Wolfenstein --- how far this result carries over to divisibility semigroups and divisibility semiloops.

AMS Subject Classification (1991): 06F

Keyword(s): lattice monoids, lattice loops, divisibility, decomposition

Received February 3, 1999, and in final form May 8, 2000. (Registered under 2774/2009.)