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Search: MSC category 16P60 ( Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension )

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1. CMB 2005 (vol 48 pp. 275)

Smith, Patrick F.
 Krull Dimension of Injective Modules Over Commutative Noetherian Rings 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 $1$. Categories:13E05, 16D50, 16P60

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