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<p>Besides a self-contained introduction into well quasi-orders and better quasi-orders, the focus is on how these concepts lead in a neat and quick way to some well-known facts regarding monomials and monomial ideals of a polynomial ring over a field. Not uninteresting connections emerge, such as a direct path to Dickson’s lemma for monomial ideals from Higman’s theorem for monoids of terms in the vein of Hilbert’s basis theorem in iterative form.</p>

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Well quasi-orders, better quasi-orders, and monomial ideals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月5日

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  • Gabriele Buriola,
  • Peter Schuster

摘要

Besides a self-contained introduction into well quasi-orders and better quasi-orders, the focus is on how these concepts lead in a neat and quick way to some well-known facts regarding monomials and monomial ideals of a polynomial ring over a field. Not uninteresting connections emerge, such as a direct path to Dickson’s lemma for monomial ideals from Higman’s theorem for monoids of terms in the vein of Hilbert’s basis theorem in iterative form.