… characterizations and properties of almost F-injective modules and almost flat modules.
Using the concepts of almost F-injectivity and almost flatness of modules, we present some …

… When the local ring R is of prime characteristic p, Theorems D and E apply, in particular, to
… By flatness of the completion map R −→ ̂R, a minimal set of generators for m extends to a …

… moduletheoretic constructions, connected with established classical notions such as injectivity,
projectivity, flatness, … A series of characteristics of r-regular rings which is a generalization …

… The character module HomZ(M, Q/Z) of a module M will be denoted by M∗ and the injective
hull of M by E(M). Let m, n … Thus, from the (m, n)-flatness of E(N), we have that N is (m, n)flat. …

… that a 1eft module F is f1at iff its character module HomZ(F,Q/Z) is injective. For (left) noetherian
rings we .prove the dual: the 1eft module l is injective iff i ts character module is fIat. We …

… We also analyse the quotient module PE(N)/N of an arbitrary module N in terms of flatness.
… determine the intersection of subinjectivity domains of character modules. In addition, we see …

… particular, pure injective modules over the first Weyl algebra over a field of characteristic 0) …
[G, Thm.3.6] states conditions that are equivalent to flatness of RE(RR). So, when the ring is …

… In the same way as in characteristic 0 we can take inverse images of left Dr-… Using p-filtrations
we will prove Kashiwara's equivalence in characteristic p. First we look at right D-modules. …

… as injective hulls of uniquely determined direct sums of indecomposable injective modules;
if … Finally, we will say that R has ⋆-finite character if every nonzero element of R is contained …

… In the present paper the author shall prove that flatness of R over RIP is characteristic … is
injective. The completion of R with respect to its radical and the completion of R as an R-module (…