Bitte benutzen Sie diese Referenz, um auf diese Ressource zu verweisen: doi:10.22028/D291-40372
Titel: Unification in Commutative Theories, Hilbert's Basis Theorem, and Gröbner Bases
VerfasserIn: Baader, Franz
Sprache: Englisch
Erscheinungsjahr: 1990
Erscheinungsort: Kaiserslautern
DDC-Sachgruppe: 004 Informatik
Dokumenttyp: Forschungsbericht (Report zu Forschungsprojekten)
Abstract: Unification in a commutative theory E may be reduced to solving linear equations in the corresponding semiring S(E) (Nutt (1988)). The unification type of E can thus be characterized by algebraic properties of S(E). The theory of abelian groups with n commuting homomorphisms corresponds to the semiring Z[X1,...,Xn]. Thus Hilbert’s Basis Theorem can be used to show that this theory is unitary. But this argument does not yield a unification algorithm. Linear equations in Z[X1,..,Xn] can be solved with the help of Gröbner Base methods, which thus provide the desired algorithm. The theory of abelian monoids with a homomorphism is of type zero (Baader (1988)). This can also be proved by using the fact that the corresponding semiring, namely N[X], is not noetherian. An other example of a semiring (even ring), which is not noetherian, is the ring Z<X1,...,Xn>, where X1, ..., Xn ( n > 1 ) are non-commuting indeterminates. This semiring corresponds to the theory of abelian groups with n non-commuting homomorphisms. Surprisingly, by construction of a Gröbner Base algorithm for right ideals in Z<X1,...,Xn>, it can be shown that this theory is unitary unifying.
Link zu diesem Datensatz: urn:nbn:de:bsz:291--ds-403725
hdl:20.500.11880/36388
http://dx.doi.org/10.22028/D291-40372
Schriftenreihe: SEKI-Report / Deutsches Forschungszentrum für Künstliche Intelligenz, DFKI [ISSN 1437-4447]
Band: 90,1
Datum des Eintrags: 5-Sep-2023
Fakultät: SE - Sonstige Einrichtungen
Fachrichtung: SE - DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
Professur: SE - Sonstige
Sammlung:SciDok - Der Wissenschaftsserver der Universität des Saarlandes



Alle Ressourcen in diesem Repository sind urheberrechtlich geschützt.