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http://dx.doi.org/10.4134/JKMS.j180751

MODULAR JORDAN TYPE FOR 𝕜[x, y]/(xm, yn) FOR m = 3, 4  

Park, Jung Pil (Faculty of Liberal Education Seoul National University)
Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 283-312 More about this Journal
Abstract
A sufficient condition for an Artinian complete intersection quotient S = 𝕜[x, y]/(xm, yn), where 𝕜 is an algebraically closed field of a prime characteristic, to have the strong Lefschetz property (SLP) was proved by S. B. Glasby, C. E. Praezer, and B. Xia in [3]. In contrast, we find a necessary and sufficient condition on m, n satisfying 3 ≤ m ≤ n and p > 2m-3 for S to fail to have the SLP. Moreover we find the Jordan types for S failing to have SLP for m ≤ n and m = 3, 4.
Keywords
Jordan types; strong Lefschetz property; weak Lefschetz property; Hilbert function;
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Times Cited By KSCI : 2  (Citation Analysis)
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