ABSTRACT
Let K be a field, and a finitely generated K-algebra with the PBW K-basis
. It is shown that if L is a nonzero left ideal of A with GK.dim(A∕L) = d<n ( = the number of generators of A), then L has the elimination property in the sense that V(U)∩L≠{0} for every subset
with
, where V(U) = K-span
. In terms of the structural properties of A, it is also explored when the condition GK.dim(A∕L)<n may hold for a left ideal L of A. Moreover, from the viewpoint of realizing the elimination property by means of Gröbner bases, it is demonstrated that if A is in the class of binomial skew polynomial rings or in the class of solvable polynomial algebras, then every nonzero left ideal L of A satisfies GK.dim(A∕L)< GK.dimA = n ( = the number of generators of A), thereby L has the elimination property.
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