English

Toward a Theory of Monomial Preorders

Commutative Algebra 2017-05-24 v3

Abstract

In this paper we develop a theory of monomial preorders, which differ from the classical notion of monomial orders in that they allow ties between monomials. Since for monomial preorders, the leading ideal is less degenerate than for monomial orders, our results can be used to study problems where monomial orders fail to give a solution. Some of our results are new even in the classical case of monomial orders and in the special case in which the leading ideal defines the tangent cone.

Keywords

Cite

@article{arxiv.1608.03725,
  title  = {Toward a Theory of Monomial Preorders},
  author = {Gregor Kemper and Ngo Viet Trung and Nguyen Thi Van Anh},
  journal= {arXiv preprint arXiv:1608.03725},
  year   = {2017}
}

Comments

24 pages; corrected typos, added references and an acknowledgment. The paper is accepted for publication in Mathematics of Computation

R2 v1 2026-06-22T15:18:21.042Z