The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors
in 1999 as a generalization of the notion of exact sequence. In this paper we investigate …

$\newcommand {\OO}[1]{\mathcal {O} _ {# 1}}\newcommand {\GG}{\mathcal
{G}}\newcommand {\End}{\mathrm {End}}\newcommand {\O}{\mathcal {O}} $ Let $ K/F $ be a …

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a
finitely generated R-module. In this paper, by computing the local cohomology modules and …

Let X be a scheme and M be a quasi-coherent OX-module. In this paper we introduce the
concept of trivial scheme extension denoted X∝ M which behave as the trivial ring …

In this thesis, we study the class S of all short exact sequences 0⟶ A⟶ α B⟶ C⟶ 0 where Im α
has a supplement in B, ie a minimal element in the set {V⊆ B| V+ Im α= B}. The …

Let $ R $ be a ring, $ F $ a subbifunctor of the functor Ext $^{1} _ {R}(-,-) $, $\mathcal {W} _
{F} $ a self-orthogonal class of left $ R $-modules respect to $ F $. We introduce $\mathcal …

Let $\mathcal {F} $ be a coherent $\mathcal {O} _X $-module over a complex manifold $ X $,
and let $ G $ be a vector bundle on $ X $. We describe an explicit isomorphism between two …

For two classes of right R-modules W, X such that P⊂ W⊂ X, where P is the class of
projective right R-modules, we show that there is an Avramov–Martsinkovsky type exact …

We extend the existing concepts of secondary representation of a module, coregular
sequence and attached prime ideals to the more general setting of any hereditary torsion …

We introduce and investigate in this paper a kind of Tate homology of modules over a
commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing …