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math.AC2025
Demotions of ideals in commutative rings with applications to normally torsion-freeness
Mehrdad Nasernejad, Jonathan Toledo
Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we…
math.AC2025
Criteria for the presence of the maximal ideal in the set of associated primes
Mehrdad Nasernejad, Jonathan Toledo
In this paper, we establish some criteria to detect the presence of the maximal ideal in the set of associated primes of powers of monomial ideals in the polyn…