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Those already knowledgeable about computer algebra
know that an important classical property of commutative
Gröbner Basis concerns elimination ideals.
If *G* is a Gröbner Basis with respect to an
elimination order (see Definition
11.2)
and *I* is the ideal generated by *G*, then
there exist a nested sequence of ideals

such that is a Gröbner Basis for
.
In
§,
we generalize
this to the noncommutative case.
This result is crucial to assuring that the
Gröbner Basis algorithm puts the
collection of polynomial equations into a triangular form.
Pure lex and, more generally, multigraded lex are examples of
such elimination orders.

*Helton *

Wed Jul 3 10:27:42 PDT 1996