We exactly calculated the parity-odd term of the effective action induced b
y the fermions in 2 + 1 dimensions at finite chemical potential and finite
temperature for a special class of gauge field background. It shows that ga
uge invariance is still respected. A more general class of background confi
gurations is also considered. The knowledge of the reduced 1 + 1 determinan
t is required in order to draw; exact conclusions about the gauge invarianc
e of the parity-odd term in this latter case. [S0556-2821(99)01018-8].