Resumen de Pure submodules of completely decomposable modules

H.P. Goeters, Bruce Olberding

• We examine the integral domain R with a submodule X of the quotient field Q of R such that the endomorphism ring of X is R and every rank one pure (in the sense of Matlis) submodule of a direct sum F of copies of X is isomorphic to X. Necessarily R is a GCD domain. If R is noetherian or atomic, then this property is characterized by R being a UFD.