Cyclic Division Algebras with Non-norm Elements

• 作者: Cheng j u Li Qin Yue Sunghan Bae
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 代数 元素 EULER函数 充分必要条件 空时分组码 应用程序 奇素数 分裂
• 年，卷（期）: 2014,（2）
• 页码范围: 275-283
• 页数: 9页
• 分类号: O156.4
• 语种: 中文

摘要

In this paper, we construct some cyclic division algebras (K/F,σ,γ). We obtain a necessary and sufficient condition of a non-norm elementγ provided that F = Q and K is a subfield of a cyclotomic field Q(ζpu), where p is a prime and ζpu is a pu th primitive root of unity. As an application for space time block codes, we also construct cyclic division algebras (K/F,σ, γ), where F = Q(i), i = √-1, K is a subfield of Q(ζ4pu) or Q(ζ4pu1 pu2), and γ = 1+i. Moreover, we describe all cyclic division algebras (K/F, σ, γ) such that F = Q(i), K is a subfield of L = Q(ζ4pu1, pu2) and γ= 1 +i, where [K: F] = φ(pu1 pu2)/d, d = 2 or 4, φ is the Euler totient function, and p1,p2 ≤ 100 are distinct odd primes.