2006/10/24 by Jea Man Ahn, Ahn, Jea Man, Young Hyun Cho +3
Computer Science · Mathematics · #13A02 #13C05 #13D40 #13E10 #13P10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/0610733
openalex publication_date 2006/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a standard Artinian k-algebra A=R/I, we give equivalent conditions for A to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of the generic initial ideal gin(I) of I under the reverse lexicographic order. Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by the the Hilbert function of I if A has the weak Lefschetz property. Furthermore, for the case that A is a standard Artinian k-algebra of codimension 3, we show that every graded Betti numbers of gin(I) are determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (resp. Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (resp. by the Hilbert function) of I.