On the projective dimension of torsion-free abelian groups over the ring of its endomorphisms

Let E be the ring of endomorphisms of an abelian group G, and let the group G be given the structure of a left module over the ring E in the natural way. We solve the problem of determining the projective dimension of the module.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 117–124, January, 1970.