Now showing items 1-10 of 15
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 ...
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 ...
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 ...
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) ...
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 ...
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 ...
(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 ...
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.
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 ...
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 ...