… modules which are injective over all pure embeddings, where an embedding $ A\rightarrow
B $ is said to be pure … of the rich theory around purity and pure-injectivity. The purpose of this …

… l-pure-injective module M can be characterized by the validity of the formula T X,x (M + )=H
X,x (M) for all n-pointed modules (… R (M) and S Q is an injective cogenerator. As a corollary we …

… , we have that the indecomposable pureinjective left Λ-modules form also a set. Thus, …
pure-injective left i?-module is m-generated. Conversely, let us put A: — U®RM. Then A is injective …

… It is proved that a pure-injective module over a commutative ring with unity is a … modules,
where duals are to be understood with reference to the circle group T, with induced module …

… RD-injective modules over arbitrary rings … pure-injective modules over Priifer rings and
valuation rings. Over these rings the RD-pure submodules are exactly the pure ones, where purity …

… the notion of pure injectivity of modules by introducing what we call a pure Baer injective
module. Some properties and some characterization of such modules are established. We …

… of A is strongly pure. As a first step towards the study of the finitely quasi-injective modules,
we … do not know if the strongly regular SAP modules must be direct sums of injective modules. …

… that any injective module has a direct decomposition into a directly finite and a purely
infinite … injective modules, we derive a surprisingly powerful technical result for quasi-continuous …

… S/S pure in PE(M)/S implies S = 0. Equivalently, M is a pure submodule of the pure injective
module. … We note that if E is an injective module, Hom(M, E) is pure injective [4, Lemma 2.11. …

… If IV is a pure-injective module and if A is a subset of N, we will use the notation H(A)N for
the hull of A in N (see [5, Chapter 4) or 17, Chapter 21). Let us consider the infinite string …