## Search

Now showing items 1-10 of 19

#### On pseudo semisimple rings

(World Scientific Publishing, 2013-03)

A necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right ...

#### 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 ...

#### Rings over which flat covers of simple modules are projective

(World Scientific Publishing, 2012-06)

Let R be a ring with identity. We prove that, the flat cover of any simple right R-module is projective if and only if R is semilocal and J(R) is cotorsion if and only if R is semilocal and any indecomposable flat right ...

#### Coneat submodules and coneat-flat modules

(Korean Mathematical Society, 2014)

A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism N → S can be extended to a homomorphism M → S. M is called coneat-flat if the kernel of any epimorphism Y → M → 0 ...

#### Neat-flat modules

(Taylor & Francis, 2016-01)

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y → M is neat in Y, i.e., the induced map Hom(S, Y) → Hom(S, M) is surjective for any simple right R-module S. Neat-flat right ...

#### 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 ...

#### Rad-supplements in injective modules

(Lugansk Taras Shevchenko National University, 2016)

We introduce and study the notion of Rad-sinjective modules (i.e. modules which are Rad-supplements in their injective hulls). We compare this notion with another generalization of injective modules. We show that the class ...

#### On w-local modules and Rad-supplemented modules

(Korean Mathematical Society, 2014)

All modules considered in this note are over associative commutative rings with an identity element. We show that a w-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all ...

#### Absolutely s-pure modules and neat-flat modules

(Taylor & Francis, 2015-02)

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R-module is neat-flat. A ...

#### Strongly radical supplemented modules

(Springer, 2012-01)

Zöschinger studied modules whose radicals have supplements and called these modules radical supplemented. Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing the ...