Let R be a valuation ring and let Q be its total quotient ring. It is proved that any singly
projective (respectively flat) module is finitely projective if and only if Q is maximal …

It is shown that each almost maximal valuation ring R, such that every indecomposable
injective R-module is countably generated, satisfies the following condition (C): each fp …

I. Introduction. Quasiprojective or self-projective modules have been introduced by Miyashita
[8] as a generalization of projective modules. Self-projective modules over various types of …

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂⊗ RM is the pure-
injective hull of M, for every finitely generated R-module M. Moreover R̂⊗ RM≅⊕ 1≤ k≤ …

Throughout this paper all rings considered will be commutative rings with identity. We shall
consider the consequences for a ring of the flatness of certain classes of its modules. Since …

A result of Nakayama and Skornyakov states that a ring R is an Artinian serial ring if and
only if every R-module is serial. This motivated us to study commutative rings for which every …

Henceforth we assume that Mt= T= Nt, M/T^ Q^ N/T, and that M and N are submodules of T*
with T*/M and T*/N torsion-free and divisible. Let M* he the P*-submodule of T* generated by …

A ring R with identity is a right PCQI-ring (PCI-ring) if every cyclic right R-module C≇ R is
quasi-injective (injective). Left PCQI-rings (PCI-rings) are similarly defined. Among others …

ENDOMORPHISM RINGS OF REDUCED COMPLETE TORSION-FREE MODULES OVER
COMPLETE DISCRETE VALUATION RINGS ideal of E. 375 Page 1 PROCEEDINGS OF …

ENDOMORPHISM RINGS OF REDUCED TORSION-FREE MODULES OVER COMPLETE
DISCRETE VALUATION RINGS Page 1 TRANSACTIONS OF THE AMERICAN …