# Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

## TL;DR

This paper develops an elimination theory for solvable polynomial algebras and their free modules using Gr"obner basis techniques, enabling systematic handling of left ideals and submodules.

## Contribution

It introduces a novel elimination framework for left ideals and submodules in solvable polynomial algebras based on Gr"obner basis theory.

## Key findings

- Established elimination theory for left ideals in solvable polynomial algebras.
- Developed elimination methods for submodules of free modules over these algebras.
- Extended Gr"obner basis techniques to facilitate ideal and submodule elimination.

## 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.

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Source: https://tomesphere.com/paper/1812.11491