Reduction numbers and initial ideals

Details Reduction numbers and initial ideals Reduction numbers and initial ideals

2002-10-04

arxiv.org/abs/math/0210064v1

Mathematics

Commutative Algebra

6 pages

Scientific paper

The reduction number r(A) of a standard graded algebra A is the least integer
k such that there exists a minimal reduction J of the homogeneous maximal ideal
m of A such that Jm^k=m^{k+1}. Vasconcelos conjectured that the reduction
number of A=R/I can only increase by passing to the initial ideal, i.e
r(R/I)\leq r(R/in(I)). The goal of this note is to prove the conjecture.

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