A left R-module M is called cotorsion if Ext (F, M) = 0 for every flat left R-module F. We will show that if a ring R is
cotorsion as a left module over itself and J denotes the Jacobson radical of R, then R/J is von Neumann regular,
idempotents lift modulo J, and R/J is injective as a left module over itself. (Joint work with Pedro Antonio Guil Asensio)