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Now showing items 1-10 of 19

#### On a recent generalization of semiperfect rings

(Cambridge University Press, 2008-10)

In a recent paper by Wang and Ding, it was stated that any ring which is generalized supplemented as a left module over itself is semiperfect. The purpose of this note is to show that Wang and Ding's claim is not true and ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Poor and pi-poor Abelian groups

(Taylor & Francis, 2017-01)

In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Weakly distributive modules. Applications to supplement submodules

(Indian Academy of Sciences, 2010-11)

In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive ...