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    • On generalized cyclotomic derivations

      SAKSHI GUPTA SURJEET KOUR

      Article Volume 133 Published: 6 March 2023 Article ID 0005

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/133/0005

    • Keywords

       

      Darboux polynomial; Jouanolou derivation; cyclotomic derivation.

    • Abstract

       

      In this article, we study the field of rational constants and Darboux polynomials of a generalized cyclotomic $K$-derivation $d$ of $K[X]$. It is shown that $d$ is without Darboux polynomials if and only if $K(X)^d = K$. The result is also studied in the tensor product of polynomial algebras.

    • Author Affiliations

       

      SAKSHI GUPTA1 SURJEET KOUR1

      1. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, Delhi 110 016, India

    • Dates

       
      Published
      6 March 2023
      Manuscript received
      26 August 2022
      Manuscript revised
      24 November 2022
      Accepted
      9 December 2022
      Final version published online
      6 March 2023

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