The saturation number of monomial ideals

DOI10.1080/00927872.2023.2178658zbMATH Open1517.13011arXiv2211.10982MaRDI QIDQ6157676

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Publication date: 22 June 2023

Published in: (Search for Journal in Brave)

Abstract: Let

S = m a t h b b K [x_{1}, l d o t s, x_{n}]

be the polynomial ring over a field

m a t h b b K

and

m a t h f r a k m = (x_{1}, l d o t s, x_{n})

be the irredundant maximal ideal of

S

. For an ideal

I s u b s e t S

, let

m a t h r m s a t (I)

be the minimum number

k

for which

I c o l o n m a t h f r a k m^{k} = I c o l o n m a t h f r a k m^{k + 1}

. In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables.

Full work available at URL: https://arxiv.org/abs/2211.10982

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