• A Finer Classification of the Unit Sum Number of the Ring of Integers of Quadratic Fields and Complex Cubic Fields

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      https://www.ias.ac.in/article/fulltext/pmsc/119/03/0267-0274

    • Keywords

       

      Unit; unit sum number; ring of integers; quadratic fields; complex cubic field.

    • Abstract

       

      The unit sum number, $u(R)$, of a ring 𝑅 is the least 𝑘 such that every element is the sum of 𝑘 units; if there is no such 𝑘 then $u(R)$ is 𝜔 or $\infty$ depending on whether the units generate 𝑅 additively or not. Here we introduce a finer classification for the unit sum number of a ring and in this new classification we completely determine the unit sum number of the ring of integers of a quadratic field. Further we obtain some results on cubic complex fields which one can decide whether the unit sum number is 𝜔 or $\infty$. Then we present some examples showing that all possibilities can occur.

    • Author Affiliations

       

      Nahid Ashrafi1

      1. Department of Mathematics, Semnan University, Semnan, Iran
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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