Pure submodules of completely decomposable modules

• Autores: H.P. Goeters, Bruce Olberding
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 2, 2008, págs. 373-382
• Idioma: inglés
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• Resumen

  • 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.