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<p>Let <i>A</i> be a retract of the polynomial ring in three variables over a field <i>k</i>. It is known that if char (<i>k</i>) = 0 or tr.deg<sub><i>k</i></sub><i>A</i> ≠ 2, then <i>A</i> is a polynomial ring. We give some sufficient conditions for <i>A</i> to be the polynomial ring in two variables over <i>k</i> when char (<i>k</i>) &gt; 0 and tr.deg<sub><i>k</i></sub><i>A</i> = 2.</p>

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Remarks on retracts of polynomial rings in three variables in any characteristic

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Hideo Kojima,
  • Takanori Nagamine,
  • Riko Sasagawa

摘要

Let A be a retract of the polynomial ring in three variables over a field k. It is known that if char (k) = 0 or tr.degkA ≠ 2, then A is a polynomial ring. We give some sufficient conditions for A to be the polynomial ring in two variables over k when char (k) > 0 and tr.degkA = 2.