  We analyse the Multiplicative Anomaly (MA) in the case of quantized massive
fermions coupled to a background torsion. The one-loop Effective Action (EA)
can be expressed in terms of the logarithm of determinant of the appropriate
first-order differential operator acting in the spinors space. Simple algebraic
manipulations on determinants must be used in order to apply properly the
Schwinger-DeWitt technique, or even the covariant perturbation theory
(Barvinsky and Vilkovisky, 1990), which is used in the present work. By this
method, we calculate the finite non-local quantum corrections, and analyse
explicitly the breakdown of those algebraic manipulations on determinants,
called by MA. This feature comes from the finite non-local EA, but does not
affect the results in the UV limit, in particular the beta-functions. Similar
results was also obtained in previous papers but for different external fields
(QED and scalar field).
