%0 Journal Article
%T Composition-Diamond Lemma for Modules
%A Yuqun Chen
%A Yongshan Chen
%A Chanyan Zhong
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0804.0917v1