7 papers
Strong persistence index and fluctuations in colon powers of monomial ideals
Mehrdad Nasernejad, Jonathan Toledo
Let be an ideal in a commutative Noetherian ring . We say that a positive integer is the strong persistence index of if is the smallest integer such th…
Asymptotic Properties of Filtrations of Ideals
Mehrdad Nasernejad, Jonathan Toledo
We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration , w…
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…
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…
On the copersistence property and nearly copersistence property of monomial ideals
Mehrdad Nasernejad, Jonathan Toledo
In this paper we investigate the monomial ideals which satisfy the copersistence property or nearly copersistence property.
On the strong persistence property and normally torsion-freeness of square-free monomial ideals
Alain Bretto, Mehrdad Nasernejad, Jonathan Toledo
In this paper, we first show that any square-free monomial ideal in has the strong persistence property. Next we will provide a criterion for a minimal…
Normally torsion-freeness and normality criteria for monomial ideals
M. Nasernejad, V. Crispin Quinonez, J. Toledo
In this paper, we focus on the associated primes of powers of monomial ideals and asymptotic behavior properties such as normally torsion-freeness, normality, the strong persistenc…