Ideals whose associated graded rings are isomorphic to the base rings

Mathematics – Commutative Algebra

Scientific paper

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Scientific paper

Let $k$ be a field. We determine the ideals $I$ in a finitely generated
graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$.
Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and
give the condition for $A[I t]$ to be generalized Cohen-Macaulay.

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