Strong preinjective partitions and almost split morphisms (Q5936003)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Strong preinjective partitions and almost split morphisms |
scientific article; zbMATH DE number 1612863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong preinjective partitions and almost split morphisms |
scientific article; zbMATH DE number 1612863 |
Statements
Strong preinjective partitions and almost split morphisms (English)
0 references
8 September 2002
0 references
strong preinjective partitions
0 references
almost split morphisms
0 references
pure semisimple rings
0 references
indecomposable modules
0 references
0 references
For any ring \(R\), if \(\mathcal C\) is a family of indecomposable \(R\)-modules of finite length such that \(\mathcal C\) contains a finite cogenerating set and every subfamily of \(\mathcal C\) has right almost split morphisms, then every subfamily has a unique strong preinjective partition of countable length.NEWLINENEWLINENEWLINEAs a consequence, every family of finitely generated indecomposable left modules over a left pure semisimple ring has a unique strong preinjective partition of countable length.
0 references
