  Let E_n be the n-th Lubin-Tate spectrum at a prime p. There is a commutative
S-algebra E^{nr}_n whose coefficients are built from the coefficients of E_n
and contain all roots of unity whose order is not divisible by p. For odd
primes p we show that E^{nr}_n 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
E^{nr}_n with Galois group a finite group G with cyclic quotient. Our results
carry over to the K(n)-local context.
