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math.AC2025
Koszul property and finite linearity defect over -stretched local rings
Do Van Kien, Hop D. Nguyen
The linearity defect is a measure for the non-linearity of minimal free resolutions of modules over noetherian local rings. A tantalizing open question due to Herzog and Iyengar as…
math.AC2025
Asymptotic regularity of graded families of ideals
Tai Huy Ha, Hop D. Nguyen, Thai Thanh Nguyen
We show that the asymptotic regularity of a graded family of homogeneous ideals in a reduced standard graded algebra, i.e., the limit $\lim_{n \rightarrow \infty}…