Abstract
In this paper, we construct some cyclic division algebras (K/F, σ, γ). We obtain a necessary and sufficient condition of a non-norm element γ provided that F = ℚ and K is a subfield of a cyclotomic field ℚ(ζpu), where p is a prime and ζpu is a puth 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), [Formula: see text], K is a subfield of ℚ(ζ4pu) or [Formula: see text], 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 [Formula: see text] and γ=1+i, where [Formula: see text], d = 2 or 4, φ is the Euler totient function, and p1, p2 ≤ 100 are distinct odd primes.
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