We generalize Hill's lemma in order to obtain a large family of C-filtered submodules from a
single C-filtration of a module. We use this to prove the following generalization of …

A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

Let CA, B be a bounded cotorsion theory and K be a local splitter for C. We prove that
Shelah's uniformization principle UP implies that C is not generated by K. As corollaries, we …

We will prove that if a ring R is either countable or a Prüfer domain, then n-cotilting R-
modules are pure injective. We can apply and modify a very nice argument due to Jensen …

Cotilting Modules Are Pure-Injective Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 131, Number 12, Pages 3665-3672 S 0002-9939(03)06938-7 …

We describe in homological terms the direct limit closure of a class C of modules over a ring
R. We also determine the closure of the cotorsion pair=(A, B) cogenerated by C. As an …

A classic result by Bass says that the class of all projective modules is covering if and only if
it is closed under direct limits. Enochs extended the if-part by showing that every class of …

A well-known theorem of Kaplansky states that any projective module is a direct sum of
countably generated modules. In this paper, we prove the w-version of this theorem, where …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

Let $ R $ be a subring of the rationals. We want to investigate self splitting $ R $-modules $
G $(that is $\operatorname {Ext} _R (G, G)= 0) $. Following Schultz, we call such modules …