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Now showing items 1-10 of 16

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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) ...