We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary
properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct …

In this paper, we extend the notion of C-injective module to that of C-FP-injective module,
where S CR is a semidualizing bimodule over associative rings. We first obtain a result on …

The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The
properties of both classes of rings are closely related to the embedding of finitely presented …

This paper extends many conclusions based on phantom envelopes and Ext-phantom
covers of modules, and we find that many important properties still hold after replacing …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

In this paper the n--injective (pre) envelopes and the n--projective (pre) covers are
investigated, which generalize and include some known envelopes and covers. Various …

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 …

In this paper, we study the existence of L⊥-envelopes, L-envelopes, D⊥-envelopes, D-
covers, and L-covers where L and D denote the classes of modules of injective and …