Left and right splittings of a short exact sequence

Let \(R\) be a ring, and let \[ \xi\colon 0 \to A \mapsvia{d_1} B \mapsvia{d_2} C \to 0 \] be a short exact sequence of \(R\)-modules. A right splitting of \(\xi\) is an \(R\)-linear map \(s\colon C\to B\) with \(d_2 \circ s = \id_{C}\). A left splitting of \(\xi\) is an \(R\)-linear map \(t\colon B\to A\) with \(t \circ d_1 = \id_A\).