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math.AC2004★ 1 cited
On the radical of a monomial ideal
Juergen Herzog, Yukihide Takayama, Naoki Terai
Algebraic and combinatorial properties of a monomial ideal and its radical are compared.
math.AC2004★ 2 cited
A generalized Hochster's formula for local cohomologies of monomial ideals
Yukihide Takayama
The Hilbert series of local cohomologies for monomial ideals, which are not necessarily square-free, is established. As applications, we give a sharp lower bound of the non-vanishi…
math.AC2004
Ideals whose associated graded rings are isomorphic to the base rings
Yukihide Takayama
Let be a field. We determine the ideals in a finitely generated graded -algebra , whose associated graded rings are isomorphic to . Also we compute the graded loca…