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TitleRelative Gr\"obner-Shirshov bases for algebras and groups.
Author(s) Leonid A. Bokut, K.P. Shum
TypeArticle in Journal
AbstractThe notion of a relative Gröbner-Shirshov basis for algebras and groups is introduced. The relative composition lemma and relative (composition-)diamond lemma are established. In particular, it is shown that the relative normal forms of certain groups arising from Malcev's embedding problem are the irreducible normal forms of these groups with respect to their relative Gröbner-Shirshov bases. Other examples of such groups are given by showing that any group $ G$ in a Tits system $ (G, B, N,S)$ has a relative ($ B$-)Gröbner-Shirshov basis such that the irreducible words are the Bruhat words of $ G$.
ISSN1061-0022; 1547-7371/e
URL http://www.ams.org/journals/spmj/2008-19-06/S1061-0022-08-01025-X/home.html
LanguageEnglish
JournalSt. Petersbg. Math. J.
Volume19
Number6
Pages867--881
PublisherAmerican Mathematical Society (AMS), Providence, RI
Year2008
Edition0
Translation No
Refereed No
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