Toward a theory of monomial preorders
Copyright policy )Toward a theory of monomial preorders
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.
24 pages; corrected typos, added references and an acknowledgment. The paper is accepted for publication in Mathematics of Computation
- Vietnam Academy of Science and Technology Viet Nam
- Osnabrück University Germany
toric ring, monomial order, graded invariants, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), leading ideal, descent of properties, regular locus, Computational aspects in algebraic geometry, standard basis, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), weight order, 13P10 (Primary), 14Qxx, 13H10 (Secondary), normal locus, dimension, FOS: Mathematics, monomial preorder, Cohen-Macaulay locus, flat deformation
toric ring, monomial order, graded invariants, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), leading ideal, descent of properties, regular locus, Computational aspects in algebraic geometry, standard basis, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), weight order, 13P10 (Primary), 14Qxx, 13H10 (Secondary), normal locus, dimension, FOS: Mathematics, monomial preorder, Cohen-Macaulay locus, flat deformation
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).10 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!