  In this paper we give some relationships among the Groebner-Shirshov bases in
free associative algebras, free left modules and "double-free" left modules
(free modules over a free algebra). We give the Chibrikov's Composition-Diamond
lemma for modules and show that Kang-Lee's Composition-Diamond lemma follows
from this lemma. As applications, we also deal with highest weight module over
the Lie algebra $sl_2$, Verma module over a Kac-Moody algebra, Verma module
over Lie algebra of coefficients of a free conformal algebra and the universal
enveloping module for a Sabinin algebra.
