  We study dynamo action in a convective layer of electrically-conducting,
compressible fluid, rotating about the vertical axis. At the upper and lower
bounding surfaces, perfectly-conducting boundary conditions are adopted for the
magnetic field. Two different levels of thermal stratification are considered.
If the magnetic diffusivity is sufficiently small, the convection acts as a
small-scale dynamo. Using a definition for the magnetic Reynolds number $R_M$
that is based upon the horizontal integral scale and the horizontally-averaged
velocity at the mid-layer of the domain, we find that rotation tends to reduce
the critical value of $R_M$ above which dynamo action is observed. Increasing
the level of thermal stratification within the layer does not significantly
alter the critical value of $R_M$ in the rotating calculations, but it does
lead to a reduction in this critical value in the non-rotating cases. At the
highest computationally-accessible values of the magnetic Reynolds number, the
saturation levels of the dynamo are similar in all cases, with the mean
magnetic energy density somewhere between 4 and 9% of the mean kinetic energy
density. To gain further insights into the differences between rotating and
non-rotating convection, we quantify the stretching properties of each flow by
measuring Lyapunov exponents. Away from the boundaries, the rate of stretching
due to the flow is much less dependent upon depth in the rotating cases than it
is in the corresponding non-rotating calculations. It is also shown that the
effects of rotation significantly reduce the magnetic energy dissipation in the
lower part of the layer. We also investigate certain aspects of the saturation
mechanism of the dynamo.
