On the stable set of associated prime ideals of a monomial ideal
Shamila Bayati, J\"urgen Herzog, Giancarlo Rinaldo
TL;DR
This paper demonstrates that any nonzero monomial prime ideals can be realized as the stable set of associated primes of a monomial ideal and provides an algorithm to compute this set.
Contribution
It introduces a method to realize any set of nonzero monomial prime ideals as the stable associated primes of a monomial ideal and presents an algorithm for computation.
Findings
Any set of nonzero monomial prime ideals can be realized as a stable set.
An explicit algorithm for computing the stable set is provided.
The results deepen understanding of the structure of monomial ideals.
Abstract
It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Polynomial and algebraic computation