Department of Mathematics
Server

A classical result due to E.Matlis says that over a left Noetherian ring every injective left module is a direct sum of indecomposable injective left modules. If K is a field, s an automorphism of K, and ð a s-derivation of K, then we can construct the skew polynomial ring R=K[x;s,ð], which is a left and right Euclidean domain, and hence is left (and right) noetherian.

Motivated by a classic treatment of O.Ore, we take advantage of some factorization and decomposition theorems in R and present a nice description of the internal structure of an indecomposable injective module E. A consideration of the R-action on E and of the arithmetic of R on an element-by-element basis leads to a localization of R that allows us to describe the structure of E and determine its socle series.