In trying to extend the concept of torsion to rings more general than commutative integral
domains the first thing that we notice is that if the definition is carried over word for word …

When we consider modules A over a ring R which is not a commutative integral domain, the
usual torsion theory becomes somewhat inadequate, since zero-divisors of R are …

Torsionfree injective modules Page 1 Pacific Journal of Mathematics TORSIONFREE
INJECTIVE MODULES MARK LAWRENCE TEPLY Vol. 28, No. 2 April 1969 Page 2 PACIFIC …

In the usual torsion theory over a commutative integral domain R, a significant place is
occupied by the question of when “the torsion submodule t (M) of an R-module M is a direct …

The subject of torsion-free modules over an arbitrary integral domain arises naturally as a
generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his …

The idea of a torsion element of an abelian group extends naturally enough to modules over
integral domains, but for modules over an arbitrary ring there seem to be a number of …

In a fundamental paper [1], BAv.~ proved a number of definitive results concerning the
splitting off of the torsion subgroup of an abelian group. Not much has since been added to …

LetRbe a ring. AnR-moduleM is called a (weak) duo moduleprovided every (direct
summand) submodule of M is fully invariant. It is proved that if R is a commutative domain …

Introduction. Let R be an integral domain with quotient field Q, and let A be a module over R.
A is said to be a divisible R-module, if rA= A for every r7OER. An element xEA is said to be a …

A module is extending (or has the property (Q)) if every complement submodule is a direct
summand. We prove that a module over a commutative domain has this property, if and only …