Composition-Diamond Lemma for Modules

Details Composition-Diamond Lemma for Modules Composition-Diamond Lemma for Modules

2008-04-06

arxiv.org/abs/0804.0917v1

Czech J Math, 60(135)(2010), 59-76.

Mathematics

Rings and Algebras

Scientific paper

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.

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