Let k be a differential field having an algebraically closed field of constants, E be a strongly normal extension of k, and k⁰ be the algebraic closure of k in E. We prove for any intermediate differential field k K E that there is an intermediate differential field k M K such that either M is generated as a differential field over k by a nonalgebraic solution of a Riccati differential equation over k or k⁰M is an abelian extension of k⁰. Using this result, we reprove and extend certain results of Goldman and Singer and study d-solvability of linear differential equations. We also extend a result of Rosenlicht and study algebraic dependency of solutions of algebraic differential equations.
Kumbhakar et al. (Tue,) studied this question.