  In this paper we study certain category of smooth modules for reductive
$p$--adic groups analogous to the usual smooth complex representations but with
the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some
fundamental results in these settings, and as an example we give a
classification of admissible unramified irreducible representations proving by
reduction to the complex case that if the space of $K$--invariants is finite
dimensional in an irreducible smooth unramified representation that the
representation is admissible.
