In this paper, we construct some cyclic division algebras (K/F,sigma,gamma). We obtain a necessary and sufficient condition of a non-norm element gamma provided that F = Q and K is a subfield of a cyclotomic field Q(zeta p(u)), where pisaprime and zeta p(u) is a p(u) th primitive root of unity. As an application for space time block codes, we alsoconstruct cyclic division algebras (K/F, sigma, gamma), where F = Q(i), i root-1, K is a subfield of Q (zeta 4p(u)) or Q (zeta 4p(1)(u)p(2)(v)) , and gamma = 1+i. Moreover, we describe all cyclic division algebras (K/F, sigma, gamma) such that F = Q(i), K is a subfield of L = Q(zeta 4p(1)(u)p(2)(v)) and gamma = 1+i, where [K : F] = phi(p(1)(u)p(2)(v))/d, d = 2 or 4, phi is the Euler totient function, and p(1), p(2) <= 100 are distinct odd primes.

- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD

- Issue Date
- 2014-06

- Language
- English

- Article Type
- Article

- Citation
ALGEBRA COLLOQUIUM, v.21, no.2, pp.275 - 283

- ISSN
- 1005-3867

- Appears in Collection
- MA-Journal Papers(저널논문)

- Files in This Item

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