Tokyo Journal of Mathematics

Upper Bounds for the Arithmetical Ranks of Monomial Ideals


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We prove some generalization of a lemma by Schmitt and Vogel which yields the arithmetical rank in cases that could not be settled by the existing methods. Our results are based on divisibility conditions and exploit both combinatorial and linear algebraic considerations. They mainly apply to ideals generated by monomials.

Article information

Tokyo J. Math., Volume 35, Number 1 (2012), 23-34.

First available in Project Euclid: 19 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A15: Ideals; multiplicative ideal theory
Secondary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]


MONGELLI, Pietro. Upper Bounds for the Arithmetical Ranks of Monomial Ideals. Tokyo J. Math. 35 (2012), no. 1, 23--34. doi:10.3836/tjm/1342701342.

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