  We study properties of semi-elementary imsets and elementary imsets
introduced by Studeny (2005). The rules of the semi-graphoid axiom
(decomposition, weak union and contraction) for conditional independence
statements can be translated into a simple identity among three semi-elementary
imsets. By recursively applying the identity, any semi-elementary imset can be
written as a sum of elementary imsets, which we call a representation of the
semi-elementary imset. A semi-elementary imset has many representations. We
study properties of the set of possible representations of a semi-elementary
imset and prove that all representations are connected by relations among four
elementary imsets.
