Now showing items 1-10 of 18
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 ...
(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
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
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 ...
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 ...