Endomorphism rings of simple modules and block decomposition
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913610330013696 |
|---|---|
| author | Krasula, Dominik |
| author_facet | Krasula, Dominik |
| contents | A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterisation is used to study simple R-modules in terms of their Ext groups. It is shown that if R is indecomposable, all its simple modules are either finite or have the same infinite cardinality and their endomorphism rings have the same characteristics. The results are further strengthened in the case when R is quasi-Frobenius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endomorphism rings of simple modules and block decomposition Krasula, Dominik Rings and Algebras 16S50, 16L30 (Primary) 16P40, 16L60 (Secondary) A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterisation is used to study simple R-modules in terms of their Ext groups. It is shown that if R is indecomposable, all its simple modules are either finite or have the same infinite cardinality and their endomorphism rings have the same characteristics. The results are further strengthened in the case when R is quasi-Frobenius. |
| title | Endomorphism rings of simple modules and block decomposition |
| topic | Rings and Algebras 16S50, 16L30 (Primary) 16P40, 16L60 (Secondary) |
| url | https://arxiv.org/abs/2406.13582 |