An $n$-dimensional CW complex with a single $n$-cell is **reducible** if the projection $X \to X/X^{(n-1)} = S^n$ onto the top cell admits a section up to homotopy.  It is **stably reducible**, or **S-reducible**, if such a section exists for the associated suspension spectra.  An early use of this term is in

    James, I. M.
    Spaces associated with Stiefel manifolds.
    Proc. London Math. Soc. (3) 9 (1959), 115–140. 

The dual notions (**coreducible** and **S-coreducible**) appear in

    Atiyah, M. F.
    Thom complexes.
    Proc. London Math. Soc. (3) 11 (1961), 291–310. 

These ideas play a role in Adams' solution of the vector fields on spheres problem.

    Adams, J. F.
    Vector fields on spheres.
    Ann. of Math. (2) 75 (1962), 603–632.