On the existence of $\lambda $-projective splitters

Abstract.

Let D be an R-module over an arbitrary ring R of projective dimension at most 1. We construct an R-module G containing D such that Ext(D, G) = 0 = Ext(G, G). Moreover, we show that if D is $\lambda$-projective over a hereditary ring R, for some infinite cardinal $\lambda$, then G is also $\lambda$-projective.