"Gr\"{o}bner Bases in Fractional Polynomial Rings and their Applications"

    Giuseppa Carra'-Ferro.
    Department  of Mathematics, University of Catania,  Italy
    Viale Andrea Doria 6
    Catania, 95125
    Italy
    E-mail:carra@dipmat.unict.it
	
A fractional polynomial is a generalization of a polynomial, in which
nonnegative rational exponents are allowed \cite{WA1}. Many properties
of polynomial rings are not true any more in this generalization,
while some other property holds. In particular, given a finitely
generated ideal I in a fractional polynomial ring with coefficients in
a field, it is possible to extend the notion of Gr\"{o}bner basis. The
aim of the paper is to show this extensions and its use for solving
fractional polynomial systems.