Clean coalgebras and clean comodules of finitely generated projective modules
Let \(R\) be a commutative ring with multiplicative identity and \(P\) is a finitely generated projective \(R\)-module. If \(P^{\ast}\) is the set of \(R\)-module homomorphism from \(P\) to \(R\), then the tensor product \(P^{\ast}\otimes_{R}P\) can be considered as an \(R\)-coalgebra. Furthermore,...
Gespeichert in:
| Datum: | 2021 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2021
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1415 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543378887409664 |
|---|---|
| author | Puspita, N. P. Wijayanti, I. E. Surodjo, B. |
| author_facet | Puspita, N. P. Wijayanti, I. E. Surodjo, B. |
| author_sort | Puspita, N. P. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-07-19T08:39:30Z |
| description | Let \(R\) be a commutative ring with multiplicative identity and \(P\) is a finitely generated projective \(R\)-module. If \(P^{\ast}\) is the set of \(R\)-module homomorphism from \(P\) to \(R\), then the tensor product \(P^{\ast}\otimes_{R}P\) can be considered as an \(R\)-coalgebra. Furthermore, \(P\) and \(P^{\ast}\) is a comodule over coalgebra \(P^{\ast}\otimes_{R}P\). Using the Morita context, this paper give sufficient conditions of clean coalgebra \(P^{\ast}\otimes_{R}P\) and clean \(P^{\ast}\otimes_{R}P\)-comodule \(P\) and \(P^{\ast}\). These sufficient conditions are determined by the conditions of module \(P\) and ring \(R\). |
| first_indexed | 2025-12-02T15:42:10Z |
| format | Article |
| id | admjournalluguniveduua-article-1415 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:10Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-14152021-07-19T08:39:30Z Clean coalgebras and clean comodules of finitely generated projective modules Puspita, N. P. Wijayanti, I. E. Surodjo, B. clean coalgebra, clean comodule, finitely generated projective module, Morita context 16T15, 16D90, 16D40 Let \(R\) be a commutative ring with multiplicative identity and \(P\) is a finitely generated projective \(R\)-module. If \(P^{\ast}\) is the set of \(R\)-module homomorphism from \(P\) to \(R\), then the tensor product \(P^{\ast}\otimes_{R}P\) can be considered as an \(R\)-coalgebra. Furthermore, \(P\) and \(P^{\ast}\) is a comodule over coalgebra \(P^{\ast}\otimes_{R}P\). Using the Morita context, this paper give sufficient conditions of clean coalgebra \(P^{\ast}\otimes_{R}P\) and clean \(P^{\ast}\otimes_{R}P\)-comodule \(P\) and \(P^{\ast}\). These sufficient conditions are determined by the conditions of module \(P\) and ring \(R\). Lugansk National Taras Shevchenko University 2021-07-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1415 10.12958/adm1415 Algebra and Discrete Mathematics; Vol 31, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1415/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1415/555 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1415/873 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | clean coalgebra clean comodule finitely generated projective module Morita context 16T15 16D90 16D40 Puspita, N. P. Wijayanti, I. E. Surodjo, B. Clean coalgebras and clean comodules of finitely generated projective modules |
| title | Clean coalgebras and clean comodules of finitely generated projective modules |
| title_full | Clean coalgebras and clean comodules of finitely generated projective modules |
| title_fullStr | Clean coalgebras and clean comodules of finitely generated projective modules |
| title_full_unstemmed | Clean coalgebras and clean comodules of finitely generated projective modules |
| title_short | Clean coalgebras and clean comodules of finitely generated projective modules |
| title_sort | clean coalgebras and clean comodules of finitely generated projective modules |
| topic | clean coalgebra clean comodule finitely generated projective module Morita context 16T15 16D90 16D40 |
| topic_facet | clean coalgebra clean comodule finitely generated projective module Morita context 16T15 16D90 16D40 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1415 |
| work_keys_str_mv | AT puspitanp cleancoalgebrasandcleancomodulesoffinitelygeneratedprojectivemodules AT wijayantiie cleancoalgebrasandcleancomodulesoffinitelygeneratedprojectivemodules AT surodjob cleancoalgebrasandcleancomodulesoffinitelygeneratedprojectivemodules |