4 papers
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…
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…