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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.
Categories:16D50, 16L60 |
3. CMB 1998 (vol 41 pp. 261)
A simple ring over which proper cyclics are continuous is a $\PCI$-ring It is shown that simple rings over which proper cyclic right modules are
continuous coincide with simple right $\PCI$-rings, introduced by Faith.
Keywords:Simple rings, $\PCI$-rings, $\PCQI$-rings, continuous modules,, quasi-continuous modules Categories:16D50, 16D70 |