In the present thesis we study basics of algebraic treatment of linear
time-varying differential equations with meromorphic coefficients. For that
we introduce the ring of linear differential operators with meromorphic
coefficients as a skew polynomial ring. Using greatest common divisors and
least common multiples, a quotient division ring is constructed, which
proves to be useful when working with matrices. The Jacobson form of these
matrices and the corresponding transformations are presented, by which a
simple normal form is obtained. We use the space of almost-everywhere
smooth functions as a left module of the considered ring. It is shown that
this posesses the injective cogenerator property. The presented results'
possibility of application is demonstrated by using them to prove some
system theoretical theorems.