On the Brauer group of a two-dimensional local field.

The two-dimensional local field K = F _q(( u))(( t)), char K = p, and its Brauer group Br( K) are considered. It is proved that, if L = K( x) is the field extension for which we have x ^p − x = ut ^{− p} =: h, then the condition that ( y, f | h]_K = 0 for any y ε K is equivalent to the condition f ε Im(Nm( L*)). [ABSTRACT FROM AUTHOR]