We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answe...

In the present paper new criteria for classes of FP -injective and weakly quasi-Frobenius rings are given. Properties of both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we describe classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (resp. we...

The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...

LetR be a ring andM a rightR-module with S= End(MR). The moduleM is called almost principally quasi-injective (or APQ-injective for short) if, for any m∈M, there exists an S-submodule Xm of M such that lMrR(m) = Sm ⊕ Xm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any s∈ S, there exists a left ideal Xs of S such that lS(ker(s)) = Ss ⊕ Xs. In thi...

We prove that every first-order formula that is invariant under quasi-injective bisimulations is equivalent to a formula of the hybrid logic H{↓}. Our proof uses a variation of the usual unravelling technique. We also briefly survey related results, and show in a standard way that it is undecidable whether a first-order formula is invariant under quasi-injective bisimulations.

‎for the subclasses ${mathcal m}_1$ and ${mathcal m}_2$ of‎‎monomorphisms in a concrete category $mathcal c$‎, ‎if ${mathcal‎‎m}_2subseteq {mathcal m}_1$‎, ‎then ${mathcal m}_1$-injectivity‎‎implies ${mathcal m}_2$-injectivity‎. ‎the baer type criterion is about‎ ‎the converse of this fact‎. ‎in this paper‎, ‎we apply injectivity to the classes of {it $c$-dense‎, ‎$c$-closed}‎ ‎monomorphisms‎. ...