10.44 (1986)

Prove that every standard homomorphism (see 10.43 for definition) $\Lambda$ of $E_n(R) \subset GL_n(R) = GL(V)$ into $E_m(S) \subset GL_m(S) = GL(W)$ originates from a collineation and a correlation, that is, has the form $\Lambda x = (g^{-1}xg)f + (h^{-1}xh)(1 - f)$, where $g$ is a semilinear isomorphism $V_R \to W_S$ (collineation) and $h$ is a semilinear isomorphism $V_R \to {}_S W'_{S_0}$ (correlation).