46.2 Definition. An R-module J is an injective module if J satisfies one of the equivalent conditions of Proposition 46.1. 46.3 Theorem (Baer's Criterion).
Define an iMiomomorphism. ?:xR n N-+L by A(z)=cr(z) zexR CN. As xR^L and L is quasi-injective
Algebraic compactness can be defined in the same way as in 3 by using this definition of purity. I'. Next we prove Theorem 2 for this algebraic compactness. Let
applying this general theory to functors ® and Horn we define the notion of faithfully projective modules [Definition 2] and faithfully injective modules.
27 sept. 2004 Proof. Let F be a non-zero fp-injective module. ... The following theorem allows us to give examples of valuation rings that are. IF-rings.
INJECTIVE MODULES. Definition 1.1. An R-module E is injective if for all R-module homomor- phisms ? : M ?? N and ? : M ?? E where ? is injective
Definition 2. Let A and B be modules over a ring R. A function f : A ??. B is an R-module homomorphism provided that for
Thus the definition of divisible means in some rough sense that any element of the module may be divided by an arbitrary nonzero element of the ring. Lemma 2.
https://comptes-rendus.academie-sciences.fr/mathematique/item/10.5802/crmath.306.pdf
26 sept. 2008 The concept of algebraic compactness appears at first