We obtain a characterization of left perfect rings via superstability the class flat modules with pure embeddings. $\mathbf{Theorem.}$ For ring $R$ following are equivalent. - is perfect. The $R$-modules embeddings superstable. There exists $\lambda \geq (|R| + \aleph_0)^+$ such that has uniqueness limit models cardinality $\lambda$. Every model in $\Sigma$-cotorsion. A key step our argum...

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For a prime number p > 2, we give a direct proof of Breuil’s classification of killed by p finite flat group schemes over the valuation ring of a p-adic field with perfect residue field. As application we prove that the Galois modules of geometric points of such group schemes and of their characteristic p analogues coming from Faltings’s strict modules can be identified via the Fontaine-Wintenb...

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any right R-module over an associative ring R with an identity element. We show that a right R-module M is pure-projective if and only if there exists an integer n ≥ 0 and a pure-exact sequence 0 → M → Pn → · · · → P0 → M → 0 with pure-projective modules Pn, . . . , P0. As a consequence we get the following v...

for each f, g ∈ L (G). For the theory of this Banach algebra, see [8], [14], [17], and [2, §3.3], for example. There are many standard left (and right) Banach L(G)-modules. Here we determine when these modules have certain well-known homological properties; we shall summarize some known results, and establish various new ones. In fact, we are seeking to characterize the locally compact groups G...

In this paper, some familiar and new results on arithmetical rings, modules, Bezout rings (not necessarily commutative) are provided. particular, we examine relationships between their localizations by maximal ideals, saturated submodules saturations, localizable properties of annihilators finitely generated modules over diagonalizable with flat right quasi-projective Hermite Pierce stalks, Kru...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

Recently, Yekutieli introduced projective dimension, injective dimension and flat of DG-modules by generalizing the characterization ordinary modules vanishing Ext or Tor-groups. In this paper, we introduce a DG-version projective, resolution for over connective DG-algebra which are different from known resolutions. An important feature these resolutions is that, roughly speaking, “length” give...