Work

The saturation number of monomial ideals

Year: 2023

Type: article

Abstract: Let S=K[x1,…,xn] be the polynomial ring over a field K and m=(x1,…,xn) be the homogeneous maximal ideal of S. For an ideal I⊂S, let sat(I) be the minimum number k for which I:mk=I:mk+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.

Source: Communications in Algebra

DOI: 10.1080/00927872.2023.2178658

Authors: Reza Abdolmaleki, Ali Akbar Yazdan Pour

Institutions: Institute for Advanced Studies in Basic Sciences, Institute for Research in Fundamental Sciences

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Instituto Politécnico de Macau, Institute for Research in Fundamental Sciences

Award: G5768615104