On projective free properties of rings (Q1919045)

The authors study the following properties of commutative rings: \(R\) is a finite direct product (sum) of rings over which every projective module is free (resp. free upto a projective direct summand of rank 1). -- Mostly they ask to what extent these properties are preserved under performing group rings (of abelian groups). I doubt whether there is something new in the paper. (I do not see why in the proofs of corollary 2.3 and proposition 2.3 the order of a finite group should be a unit in some ring, resp. a field).