Kulikov's criterion for modules.
Factor-splitting length of torsionfree abelian groups of rank two
A remark on hyper-indecomposable groups
Un gruppo abeliano senza torsione ed indecomponibile è detto iperindecomponibile se tutti i sottogruppi propri del suo inviluppo iniettivo che lo contengono sono indecomponibili. In questo lavoro si caratterizza la classe dei gruppi iperindecomponibili per mezzo di loro proprietà locali. I gruppi iperindecomponibili omogenei sono caratterizzati tramite la proprietà «factor-splitting».
A remark on hyper-indecomposable groups
Un gruppo abeliano senza torsione ed indecomponibile è detto iperindecomponibile se tutti i sottogruppi propri del suo inviluppo iniettivo che lo contengono sono indecomponibili. In questo lavoro si caratterizza la classe dei gruppi iperindecomponibili per mezzo di loro proprietà locali. I gruppi iperindecomponibili omogenei sono caratterizzati tramite la proprietà «factor-splitting».
On torsionfree classes which are not precover classes
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite...
Mixed abelian groups of torsion free rank one
A note on mixed abelian groups
On splitting mixed abelian groups
Pure closures
Notes on purities
On isomorphism of quasi-isomorphic torsion free Abelian groups
Completely decomposable abelian groups any regular subgroup of which is completely decomposable
[On the conference “Binary systems and ring theoretic methods in universal algebra”]
[On the conference “Binary systems and ring theoretic methods in universal algebra”]
Aplikace teorie grafů na výpočet determinantů matic speciálního typu
[On the conference on rings and modules]
The structure of primary modules
O jistých grupách matic
Relatively exact modules
Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice of submodules of a torsionfree module consisting of all submodules of such that is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application...
Non-singular precovers over polynomial rings
One of the results in my previous paper , preprint, Corollary 3, states that for every hereditary torsion theory for the category -mod with , being Goldie’s torsion theory, the class of all -torsionfree modules forms a (pre)cover class if and only if is of finite type. The purpose of this note is to show that all members of the countable set of rings have the property that the class of all non-singular left modules forms a (pre)cover class if and only if this holds for an arbitrary member...
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