Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2018.11.04
  • Accepted : 2019.07.25
  • Published : 2020.03.01
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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.

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Acknowledgement

Supported by : NRF

This paper was supported by the Basic Science Research Program of the NRF (Korea) under the grant No. NRF-2019R1F1A1056934.

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