Monomial idealstransversal intersectionGröbner basisTaylor complexminimal free resolutionsimplicial complexIn this paper, we prove conditions for transversal intersection of monomial ideals and derive a simplicial characterization of this phenomenon.doi:10.1007/s12044-019-0509-5Joydip...
Monomial idealsStanley decompositionsStanley depthWe show that the Stanley's Conjecture holds for an intersection of three monomial primary ideals of a polynomial algebra S over a field.doi:10.1214/12-BA725Andrei ZarojanuarXivBulletin mathematiques de la Societe des ences mathematiques de Roumanie...
Strong Lefschetz property initial ideals monomial ideals complete intersection Hilbert function摘要 In this paper, we study the strong Lefschetz property of artinian complete intersection ideals generated by products of linear forms. We prove the strong Lefschetz property for a class of such ideals with...
We prove that associated graded rings of complete intersection monomial curves of codimension three are Cohen–Macaulay if their defining ideals are generated by at most four elements. 关键词: commutative algebra standard bases associated graded rings monomial curves DOI: 10.1016/j.jalgebra.2007.11.02...
of germs with Newton-non-degenerate principal part when the Newton diagrams are “large enough”, i.e. they are large multiples of some other diagrams. In the case of local complete intersections we prove the corrected inequality, while in the hypersurface case we prove an even stronger ...
The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods from the theory of Diophantine linear equations with integer ...
The properties of the intersection algebra of two principal monomial ideals\nin a polynomial ring are investigated in detail. Results are obtained regarding\nthe Hilbert series and the canonical ideal of the intersection algebra using\nmethods from the theory of diophantine linear equations with integer...
Cohen-MacaulayGenerically complete intersection monomial idealsIn this article, we try to understand which generically complete intersection monomial ideals with fixed radical are CohenMacaulay. We are able to give a complete characterization for a special class of simplicial complexes, namely the Cohen...
Let $I$ be a monomial almost complete intersection ideal of a polynomial algebra $S$ over a field. Then Stanley's Conjecture holds for $S/I$ and $I$.doi:10.1186/1687-2770-2012-17Mircea CimpoeasarXivM. Cimpoeas, The Stanley conjecture on monomial almost complete intersection ideals. ...
In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when R is a polynomial ring over a field and I , J are principal monomial ideals. Specifically, we calculate the F -signature, divisor class group, and ...