One easily adapts standard Grobner basis techniques, e.g. see

Franz Pauer, Andreas Unterkircher.  
Grobner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations.  
AAECC 9, 271-291 (1999)  
http://www.springerlink.com/content/qgbwymag351atn71/fulltext.pdf

*Abstract.* We develop a basic theory of Grobner bases for ideals in the algebra
of Laurent polynomials (and, more generally, in its monomial subalgebras). For
this we have to generalize the notion of term order. The theory is applied to
systems of linear partial difference equations (with constant coefficients) on
${\mathbb Z}^n$. Furthermore, we present a method to compute the intersection of an ideal
in the algebra of Laurent polynomials with the subalgebra of all polynomials.