Let (G;G+) be a lattice-ordered abelian group with positive cone G+ and H+ a hereditary subsemigroup of G+. In [3] we introduced a closed ideal IH+ of the C-subalgebra BG+ of l1(G+) spanned by the functions f1x : x 2 G+g. Then we showed that the crossed product C-algebra B(G=H)+  G+ is realized as an induced C-algebra Ind eG H? ? B(G=H)+  (G=H)+
. In this paper, we prove the existence of the following short exact sequence of C-algebras 0 ! IH+  G+ ! B(G=H)+  G+ ! Ind eG H? ? B(G=H)+  (G=H)+
! 0 We then show that there is an isomorphism  of BH+  H+ into BG+  G+. Which leads to show some interesting non-trivial results on commutator ideals in C crossed products by hereditary subsemigroups as they involve a non-trivial extension of previous results in [1] and [2].