## Search

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 ...

#### Rad-supplemented modules

(Universita di Padova, 2010)

Let τ be a radical for the category of left R-modules for a ring R. If M is a τ-coatomic module, that is, if M has no nonzero τ-torsion factor module, then τ(M) is small in M. If V is a τ-supplement in M, then the intersection ...

#### 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 ...

#### 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 ...

#### Modules whose maximal submodules are supplements

(Hacettepe Üniversitesi, 2010)

We study modules whose maximal submodules are supplements (direct summands). For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective. We ...

#### Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions

(Mathematica Scandinavica, 2009)

In this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.

#### When δ-semiperfect rings are semiperfect

(TÜBİTAK, 2010-09)

Zhou defined δ -semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the ...

#### 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 ...

#### 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 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 ...