Lubin–Tate extensions, an elementary approach

We give an elementary proof of the assertion that the Lubin–Tate extension $L\geqslant K$ is an Abelian extension whose Galois group is isomorphic to $U_K/N_{L/K}(U_L)$ for arbitrary fields $K$ that have Henselian discrete valuation rings with finite residue fields. The term ‘elementary’ only means that the proofs are algebraic (that is, no transcedental methods are used [1], pp. 327, 332).