Composition-Diamond Lemma for Modules
Rings and Algebras
2010-03-09 v1 Quantum Algebra
Abstract
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 , 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.
Keywords
Cite
@article{arxiv.0804.0917,
title = {Composition-Diamond Lemma for Modules},
author = {Yuqun Chen and Yongshan Chen and Chanyan Zhong},
journal= {arXiv preprint arXiv:0804.0917},
year = {2010}
}