cyclic extension

cyclic extension

[′sīk·lik ik′sten·chən]
(mathematics)
A Galois extension whose Galois group is cyclic.
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To solve the ISI problem, a cyclic extension was introduced to the transmitted symbols, known as guard time, but its introduction results into loss of spectral efficiency.
The received signal is first stripped of its cyclic extension and then passed through a bank of chip matched filters, as shown in Figure 1, where
k((t)))-division algebra (K/k, [[sigma].sub.[chi]], t), where K/k is the finite cyclic extension corresponding to [chi].
Let K/k be the cyclic extension corresponding to [chi].
(iii) for k [subset] K [subset] [k.sub.cyc], the Z[[[rho].sub.K]]-ideal [[alpha].sub.K](G) is principal and if char k [not equal to] 2, then k([[zeta].sub.r(G)])/k is cyclic extension where r(G) is the highest power of 2 dividing the exponent of G.
In [6],the author studied the case when k is a quadratic field and G = E([p.sup.3]).Let p and q be distinct odd primes and k/Q a cyclic extension of degree q.
Let k/Q be a cyclic extension of degree q,and Cl(k) the ideal class group of k.
In fact, since the cyclic extension [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is unramified at all finite primes, genus theory tells the 2-part of the narrow ideal class group of Q([square root of [p.sub.1][p.sub.2]]) is a cyclic group of order [greater than or equal to] 4.
Since f(a,x) is irreducible, it follows from Theorem 2.1 that the extensions [L.sub.i]/[k.sub.1] are cyclic extensions of degree 4 and we have [k.sub.1] [not equal to] Q.
Such [k.sub.[infinity]] is a limit of cyclic extensions [k.sub.n]/k of degree [p.sup.n].
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