  In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the
Hales-Jewett theorem can be combined with a sufficiently well behaved
homomorphisms. Their work was completely algebraic in nature, where they have
used the algebra of Stone-Cech compactification of discrete semigroup. They
have proved the existence of those configurations in piecewise syndetic sets,
which is a Ramsey theoretic rich set. In our work we will show those forms are
still present in very small but Ramsey theoretic sets, (like J-set, C-set) and
our proof is purely elementary in nature.
