… Enochs [5] defines a module homomorphism f:N→M to be neat … We will call M a test for
injectivity by neatness if all nonzero … will describe rings over which every non-injective module is a …

… families of rings: those rings with nonzero maps from any non-projective module to any singular
simple module (… any two non-injective modules were considered in [Citation8]. Also, the …

… provided that the corresponding quotient functor admits a right adjoint. For each object …
non-injective. We need the following definition. If is a finitely presented -module without non-zero …

… , which classes of modules admit pauper modules. The second … in function of homomorphisms
between modules, while the … be an uniform module, if for any two non-zero submodules N,…

… A provided that the abelian group homomorphism HomR(f,M): … by a chain of non-zero maps
between modules in P0. So, let … Finally, every non-injective module in ind-R is the first term of …

… On the other hand, let M be a non-injective cocyclic module. … First, we prove that no non-zero
countable module N is … induces a quasi-homomorphism, which we call f (rp) from f (G…

… classes of non-injective simple right R-modules. Then, \(S=\… in \Gamma \) so that there is a
nonzero homomorphism \(f:nR\… ring with nonzero radical is a good ring which is not a V-ring. …

… 4.4 for I/I2 is a nonzero module over the Artinian ring R/I and, … ring homomorphism, with N
Noetherian, then h(mn) = 0, from … We first note that every non-injective ring homomorphism g : …

… for I/I2 is a nonzero module over the Artinian ring R/I and, hence… We first note that every
non-injective ring homomorphism g : … Then B admits a proper Noetherian subring B containing R. …

… 7 and 8 to the case of a non-injective flat ring epimorphism … where ψR is the ring of quotients
homomorphism in (1) as … up of the principal ideals generated by the non-zero elements of R. …