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#### Cofinitely weak supplemented modules

(Taylor & Francis, 2003-11)

We prove that a module M is cofinitely weak supplemented or briefly cws (i.e., every submodule N of M with M/N finitely generated, has a weak supplement) if and only if every maximal submodule has a weak supplement. If M ...

#### Special precovers in cotorsion theories

(Cambridge University Press, 2002-06)

A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary ...

#### Extensions of weakly supplemented modules

(Mathematica Scandinavica, 2008)

It is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is ...

#### Small supplements, weak supplements and proper classes

(Hacettepe Üniversitesi, 2016)

Let SS denote the class of short exact sequences E:0 → Af→ B → C → 0 of R-modules and R-module homomorphisms such that f(A) has a small supplement in B i.e. there exists a submodule K of M such that f(A) + K = B and f(A) ...

#### Cofinitely weak supplemented lattices

(Indian National Science Academy, 2009-10)

In this paper it is shown that an E-complemented complete modular lattice L with small radical is weakly supplemented if and only if it is semilocal. L is a cofinitely weak supplemented lattice if and only if every maximal ...

#### The proper class generated by weak supplements

(Taylor & Francis, 2014-01)

We show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules ...

#### Resolutions in cotorsion theories

(American Institute of Physics Publising, 2010)

We consider the λ- (μ-) and λ̄- (μ̄-) dimensions of modules taken under a cotorsion theory (F, C) satisfying the Hereditary Condition, and establish some inequalities between the dimensions of the modules of a short exact ...

#### Rings and modules characterized by opposites of injectivity

(Elsevier, 2014-07)

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-subinjective if every homomorphism N→M extends to some E(N)→M, where E(N) is the injective hull of N. Clearly, every module is subinjective ...

#### Cofinitely supplemented modular lattices

(Springer, 2011-10)

In this paper it is shown that a lattice L is a cofinitely supplemented lattice if and only if every maximal element of L has a supplement in L. If a/0 is a cofinitely supplemented sublattice and 1/a has no maximal element, ...