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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 ...

#### 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 ...

#### 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

(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 ...