Open Access
Fall 2012 The weak Lefschetz property for ${\mathfrak{m}}$-full ideals and componentwise linear ideals
Tadahito Harima, Junzo Watanabe
Illinois J. Math. 56(3): 957-966 (Fall 2012). DOI: 10.1215/ijm/1391178557


We give a necessary and sufficient condition for a standard graded Artinian ring of the form $K[x_{1},\ldots,x_{n}]/I$, where $I$ is an ${\mathfrak{m}}$-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for componentwise linear ideals. We also prove that the class of componentwise linear ideals and that of completely ${\mathfrak{m}}$-full ideals coincide in characteristic zero and in positive characteristic, with the assumption that $\mathrm{Gin}(I)$ w.r.t. the graded reverse lexicographic order is stable.


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Tadahito Harima. Junzo Watanabe. "The weak Lefschetz property for ${\mathfrak{m}}$-full ideals and componentwise linear ideals." Illinois J. Math. 56 (3) 957 - 966, Fall 2012.


Published: Fall 2012
First available in Project Euclid: 31 January 2014

zbMATH: 1285.13026
MathSciNet: MR3161360
Digital Object Identifier: 10.1215/ijm/1391178557

Primary: 13E10
Secondary: 13A02 , 13F20

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 3 • Fall 2012
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