Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

Huishi Li

Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

Rings and Algebras 2019-01-15 v2

Authors: Huishi Li

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.

Keywords

solvable polynomial algebra free module groebner basis elimination theory left ideal submodule

Cite

@article{arxiv.1812.11491,
  title  = {Elimination Theory for Solvable Polynomial Algebras and Their Free Modules},
  author = {Huishi Li},
  journal= {arXiv preprint arXiv:1812.11491},
  year   = {2019}
}

Comments

29 pages. The statement i_1<i_2<...<i_m<n, which appears in Proposition 2.2, in the paragraph before Theorem 2.4, in Proposition 2.5, and in the paragraph straight after the proof of Proposition 2.6, is changed to i_1<i_2<...<i_m and m<n

Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

Abstract

Keywords

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