Differential étale extensions and differential modules over differential rings

This paper studies differential square zero extensions and differential modules of a commutative differential algebra R over a differential field F where the field of constants of F is algebraically closed and of characteristic 0. All elements of R and the differential R modules and algebras considered are assumed to satisfy linear homogeneous differential equations over F. For R differentially simple, we describe the invectives, and, using that all considered differential modules are R flat, provide a criterion for all square zero extensions to be differentially split.