TY - INPR
A1 - Madlener, Klaus
A1 - Reinert, Birgit
T1 - On Gröbner Bases in Monoid and Group Rings
N2 - Following Buchberger's approach to computing a Gröbner basis of a poly-nomial ideal in polynomial rings, a completion procedure for finitely generatedright ideals in Z[H] is given, where H is an ordered monoid presented by a finite,convergent semi - Thue system (Sigma; T ). Taking a finite set F ' Z[H] we get a(possibly infinite) basis of the right ideal generated by F , such that using thisbasis we have unique normal forms for all p 2 Z[H] (especially the normal formis 0 in case p is an element of the right ideal generated by F ). As the orderingand multiplication on H need not be compatible, reduction has to be definedcarefully in order to make it Noetherian. Further we no longer have p Delta x ! p 0for p 2 Z[H]; x 2 H. Similar to Buchberger's s - polynomials, confluence criteriaare developed and a completion procedure is given. In case T = ; or (Sigma; T ) is aconvergent, 2 - monadic presentation of a group providing inverses of length 1 forthe generators or (Sigma; T ) is a convergent presentation of a commutative monoid ,termination can be shown. So in this cases finitely generated right ideals admitfinite Gröbner bases. The connection to the subgroup problem is discussed.
T3 - SEKI Report - 93,8
Y1 - 1999
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/348
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-3196
ER -