Krull Dimension of Injective Modules Over Commutative Noetherian Rings

• Autores: Patrick F. Smith
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 2, 2005, págs. 275-282
• Idioma: inglés
• DOI: 10.4153/cmb-2005-026-3
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• Resumen

  • Let R be a commutative Noetherian integral domain with field of fractions Q. Generalizing a forty-year-old theorem of E. Matlis, we prove that the R-module Q/R (or Q) has Krull dimension if and only if R is semilocal and one-dimensional. Moreover, if X is an injective module over a commutative Noetherian ring such that X has Krull dimension, then the Krull dimension of X is at most 1