Now showing items 1-5 of 5
The proper class generated by weak supplements
(Taylor & Francis, 2014-01)
We show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules ...
Hereditary rings with countably generated cotorsion envelope
Let R be a left hereditary ring. We show that if the left cotorsion envelope C(RR) of R is countably generated, then R is a semilocal ring. In particular, we deduce that C(RR) is finitely generated if and only if R is a ...
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 ...
Completely cotorsion modules
(Publishing House of the Bulgarian Academy of Sciences, 2012)
We show that any finitely generated projective cotorsion left module over a ring of left pure global dimension at most 1 is a direct sum of indecomposable direct summands. We deduce that such a ring is left cotorsion and ...
Modules over Prüfer domains which satisfy the radical formula
(Cambridge University Press, 2007-01)
In this paper we prove that if R is a Prüfer domain, then the R-module R ⊕ R satisfies the radical formula. © 2007 Glasgow Mathematical Journal Trust.