Geodesic
Krull Dimension of Injective Modules Over Commutative Noetherian Rings
Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 275-282

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2005-026-3
Mots-clés : 13E05, 16D50, 16P60 
Smith, Patrick F. Krull Dimension of Injective Modules Over Commutative Noetherian Rings. Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 275-282. doi: 10.4153/CMB-2005-026-3
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