Toward a theory of monomial preorders

Kemper, Gregor; Trung, Ngo; Van Anh, Nguyen Thi

doi:10.1090/mcom/3289

Toward a theory of monomial preorders
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by Gregor Kemper, Ngo Viet Trung and Nguyen Thi Van Anh PDF

Math. Comp. 87 (2018), 2513-2537 Request permission

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.

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