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Noncommutative elimination theory

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 tex2html_wrap_inline4486


such that tex2html_wrap_inline4490 is a Gröbner Basis for tex2html_wrap_inline4486 . 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.

Wed Jul 3 10:27:42 PDT 1996