Reduction among bracket polynomials

In this paper, we propose an SL(n)-invariant division of SL(n)-invariant polynomials by establishing an admissible order among the invariant polynomials in normal form. The invariant division leads to an invariant Gröbner basis theory. The invariant division is closely related to multivariate coordinate polynomial division. This feature leads to a proof of the result that if f₁,..., f_k are SL(n,K)-invariant where K is an arbitrary field, possibly of positive characteristic, then the invariant ideal generated by them is the intersection of the ideal generated by the f_i in the polynomial ring of coordinates with the algebra of invariants.