1. CMB 2005 (vol 48 pp. 275)
||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
2. CMB 2005 (vol 48 pp. 317)
||On Pseudo-Frobenius Rings |
It is proved here that a ring $R$ is right pseudo-Frobenius
if and only if $R $ is a right Kasch ring such that the second
right singular ideal is injective.
3. CMB 1998 (vol 41 pp. 261)