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Search: MSC category 16D50 ( Injective modules, self-injective rings [See also 16L60] )

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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

2. CMB 2005 (vol 48 pp. 317)

Yousif, Mohamed F.; Zhou, Yiqiang; Zeyada, Nasr
 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)

Barthwal, S.; Jhingan, S.; Kanwar, P.
 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 modulesCategories:16D50, 16D70
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