Serial piecewise domains
A ring \(A\) is called a piecewise domain with respect to the complete set of idempotents \(\{e_1, e_2, \ldots, e_m\}\) if every nonzero homomorphism \(e_iA \rightarrow e_jA\) is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | A ring \(A\) is called a piecewise domain with respect to the complete set of idempotents \(\{e_1, e_2, \ldots, e_m\}\) if every nonzero homomorphism \(e_iA \rightarrow e_jA\) is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary (or semihereditary) rings are equivalent. We prove that a serial right Noetherian ring is a piecewise domain if and only if it is right hereditary. And we prove that a serial ring with right Noetherian diagonal is a piecewise domain if and only if it is semihereditary. |
|---|