Abstract
In this note we show by an example that the answer is negative, namely that f. —g, does not always hold. We also consider the case R = K[G^ where K is a field, and show that the answer is negative if and only if the characteristic of the field K divides the order of G when G is a finite group. We also obtain some condition for an infinite group G. If 1. 1 were true, then the arguments of Morimoto in [3], which computes a homology class of the torsion invariant (cf, Theorem 8. 4 of Dovermann-Rothenberg [2]), would be considerably simplified. Thus the negativeness of 1. 1 suggests that we cannot do without delicate arguments as in [3] in computing torsion invariants. The author would like to thank M. Morimoto, T. Matumoto and K. Motose for valuable conversations. He would also like to thank
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