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

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019