Let En be the n-th Lubin-Tate spectrum at a prime p. There is a commutative S-algebra Ennr whose coefficients are built from the coefficients of En and contain all roots of unity whose order is not divisible by p. For odd primes p we show that Ennr does not have any non-trivial connected finite Galois extensions and is thus separably closed in the sense of Rognes. At the prime 2 we prove that there are no non-trivial connected Galois extensions of Ennr with Galois group a finite group G with cyclic quotient. Our results carry over to the K(n)-local context.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 3, pp.27-43.