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 key 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.

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.