… integral domain and M a torsion-free R-module which is a direct sum of modules of countable
rank, then any direct summand of M is likewise a direct sum of modules of countable rank. …

… if and only if the direct sum of any two simple-direct-projective modules is again simple-…
that the direct sum of simple-direct-projective modules need not be simple-direct-projective. …

… Every finitely generated module is quasi-projective; … The direct sum of every pair of
quasiprojective … The direct sum of two quasi-projective modules is always quasi…

… Since B is the support algebra of M, there exists some direct summand Mj of M with Hom (M;,
I) # O, thus we obtain Mj. =~ I ~ rB M~, impossible. This shows that M as a B-…

… modules have the SSP and give an answer when the module is supposed to be a direct sum
… of whether a quasiprojective module has the SSP (or a quasi-injective module has the SIP) …

… v∈U Cv ), where the Cu are injective modules and Cv are projective modules. By Kaplansky
[9], we know that each projective module is a direct sum of countably generated modules. …

… that direct summands of pure-direct-projective right R-modules are pure-direct-projective (…
and the converse is true when the direct sum of two pure-direct-projective right R-modules …

… of a countably infinite direct sum, P, of nonzero countably generated projective modules. We
must … But this is evident from the remark above since an infinite direct sum cannot be finitely …

… to study the direct sum of indecomposable projective modules which has … direct sums of
indecomposable projective modules and, particularly, the ring over which all projective modules …

… sums of M-injective modules and projective modules in σ[M]. … via direct sums of injective
modules and projective modules. … of the direct sum of injective right R-modules is projective if …