  We evaluate the noncommutative Chern-Simons action induced by fermions
interacting with an Abelian gauge field in a noncommutative massive Thirring
model in (2+1)-dimensional spacetime. This calculation is performed in the
Dirac and Majorana representations. We observe that in Majorana representation
when $\theta$ goes to zero we do not have induced Chern-Simons term in the
dimensional regularization scheme.
