Flat covers of representations of the quiver A∞
Rooted quivers are quivers that do not contain A∞≡⋯→•→• as a subquiver. The existence of flat covers and cotorsion envelopes for representations of these quivers have been studied by Enochs et al. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for representati...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203205391 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849308788095451136 |
|---|---|
| author | E. Enochs S. Estrada J. R. García Rozas L. Oyonarte |
| author_facet | E. Enochs S. Estrada J. R. García Rozas L. Oyonarte |
| author_sort | E. Enochs |
| collection | DOAJ |
| description | Rooted quivers are quivers that do not contain
A∞≡⋯→•→• as a subquiver. The existence of flat covers and cotorsion envelopes
for representations of these quivers have been studied by Enochs et al. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for
representations of A∞. We first characterize finitely generated projective representations of A∞. We also see that there are no
projective covers for representations of A∞, which adds more
interest to the problem of the existence of flat covers. |
| format | Article |
| id | doaj-art-179723fc36cc41e5b018017e28c326ee |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-179723fc36cc41e5b018017e28c326ee2025-08-20T03:54:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003704409441910.1155/S0161171203205391Flat covers of representations of the quiver A∞E. Enochs0S. Estrada1J. R. García Rozas2L. Oyonarte3Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USADepartamento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, SpainDepartamento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, SpainDepartamento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, SpainRooted quivers are quivers that do not contain A∞≡⋯→•→• as a subquiver. The existence of flat covers and cotorsion envelopes for representations of these quivers have been studied by Enochs et al. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for representations of A∞. We first characterize finitely generated projective representations of A∞. We also see that there are no projective covers for representations of A∞, which adds more interest to the problem of the existence of flat covers.http://dx.doi.org/10.1155/S0161171203205391 |
| spellingShingle | E. Enochs S. Estrada J. R. García Rozas L. Oyonarte Flat covers of representations of the quiver A∞ International Journal of Mathematics and Mathematical Sciences |
| title | Flat covers of representations of the quiver A∞ |
| title_full | Flat covers of representations of the quiver A∞ |
| title_fullStr | Flat covers of representations of the quiver A∞ |
| title_full_unstemmed | Flat covers of representations of the quiver A∞ |
| title_short | Flat covers of representations of the quiver A∞ |
| title_sort | flat covers of representations of the quiver a∞ |
| url | http://dx.doi.org/10.1155/S0161171203205391 |
| work_keys_str_mv | AT eenochs flatcoversofrepresentationsofthequivera AT sestrada flatcoversofrepresentationsofthequivera AT jrgarciarozas flatcoversofrepresentationsofthequivera AT loyonarte flatcoversofrepresentationsofthequivera |