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<p>We characterize the nontriviality of the module of relations of an irreducible quartic polynomial in terms of a quotient between its roots. In the case where the base field is <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10474_2025_1541_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation>, we also give a characterization in terms of the roots of the cubic resolvent of the polynomial.</p>

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Nontriviality of the module of relations for degree 4 polynomials

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Á Serrano Holgado

摘要

We characterize the nontriviality of the module of relations of an irreducible quartic polynomial in terms of a quotient between its roots. In the case where the base field is \(\mathbb{Q}\) Q , we also give a characterization in terms of the roots of the cubic resolvent of the polynomial.