Computation of the mapping of factorization by the radical for $K^+_0$ of the endomorphism ring

In the paper, the mapping of factorization by the radical is computed for the semigroup of projective, finitely generated modules over the endomorphism ring of an almost completely decomposable torsion-free Abelian group of finite rank that is divisible by almost all prime numbers. Also, an answer is given to the question concerning the collections of groups of rank 1 for which one can construct an almost completely decomposable group, indecomposable as an object in $\bar M^p$, by adding a generator.