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...
Saved in:
| Date: | 2018 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543275196874752 |
|---|---|
| author | Gubareni, Nadiya Khibina, Marina |
| author_facet | Gubareni, Nadiya Khibina, Marina |
| author_sort | Gubareni, Nadiya |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T12:35:55Z |
| description | 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. |
| first_indexed | 2026-02-08T08:00:38Z |
| format | Article |
| id | admjournalluguniveduua-article-868 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:38Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-8682018-03-21T12:35:55Z Serial piecewise domains Gubareni, Nadiya Khibina, Marina piecewise domain, hereditary ring, semihereditary ring, serial ring, Noetherian diagonal, prime radical, prime quiver 16P40, 16G10 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 Algebra and Discrete Mathematics; Vol 6, No 4 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868/398 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 Gubareni, Nadiya Khibina, Marina Serial piecewise domains |
| title | Serial piecewise domains |
| title_full | Serial piecewise domains |
| title_fullStr | Serial piecewise domains |
| title_full_unstemmed | Serial piecewise domains |
| title_short | Serial piecewise domains |
| title_sort | serial piecewise domains |
| topic | piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 |
| topic_facet | piecewise domain hereditary ring semihereditary ring serial ring Noetherian diagonal prime radical prime quiver 16P40 16G10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/868 |
| work_keys_str_mv | AT gubareninadiya serialpiecewisedomains AT khibinamarina serialpiecewisedomains |