Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

Abstract

Let $K$ be a field, and $A=K[a_1,\ldots ,a_n]$ a solvable polynomial algebra in the sense of [K-RW, {\it J. Symbolic Comput.}, 9(1990), 1--26]. Based on the Gr\"obner basis theory for $A$ and for free modules over $A$, an elimination theory for left ideals of $A$ and an elimination theory for submodules of free $A$-modules are established.