Proceedings Mathematical Sciences | |
A Finer Classification of the Unit Sum Number of the Ring of Integers of Quadratic Fields and Complex Cubic Fields | |
Nahid Ashrafi1  | |
[1] Department of Mathematics, Semnan University, Semnan, Iran$$ | |
关键词: Unit; unit sum number; ring of integers; quadratic fields; complex cubic field.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
The unit sum number, $u(R)$, of a ring 𑅠is the least 𑘠such that every element is the sum of 𑘠units; if there is no such 𑘠then $u(R)$ is 𜔠or ∞ depending on whether the units generate 𑅠additively 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 𜔠or ∞. Then we present some examples showing that all possibilities can occur.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040506843ZK.pdf | 212KB | download |