Multigraded algebras and non-associative Gröbner bases

  • The basic notions of a theory of Gröbner bases for ideals in the non-associative, noncommutative algebras K{X} and K{X}\(_\infty\) with a unit freely generated by a set X over a field K are discussed. The monomials in this algebras can be identified with PB(X), the set of isomorphism classes of X-labelled finite, planar binary rooted trees, and PRT(X), the set of isomorphism classes of X-labelled finite, planar reduced rooted trees respectively, where X is the set of free algebra generators. The reduced Gröbner basis of the ideal J of relations in the Cayley algebra with respect to a chosen admissible order is computed. The multihomogeneous polynomials of multidegree (2,1,1) in the reduced Gröbner basis of the alternator ideal is computed. Some computations are obtained on Gröbner bases of ideals by use of computer programs Magma and MuPAD.

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Metadaten
Author:Saeed RajaeeORCiDGND
URN:urn:nbn:de:hbz:294-16386
Referee:Lothar GerritzenGND, Ralf HoltkampGND
Document Type:Doctoral Thesis
Language:English
Date of Publication (online):2006/07/04
Date of first Publication:2006/07/04
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Granting Institution:Ruhr-Universität Bochum, Fakultät für Mathematik
Date of final exam:2006/05/17
Creating Corporation:Fakultät für Mathematik
GND-Keyword:Hilbert-Funktion; Cayley-Algebra; PI-Algebra; Reduktionssystem; MuPAD
Dewey Decimal Classification:Naturwissenschaften und Mathematik / Mathematik
faculties:Fakultät für Mathematik
Licence (German):License LogoKeine Creative Commons Lizenz - es gelten der Veröffentlichungsvertrag und das deutsche Urheberrecht

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