On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings
In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this proper...
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2023-10-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/2948 |
| _version_ | 1797404901616123904 |
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| author | Eltiyeb Ali |
| author_facet | Eltiyeb Ali |
| author_sort | Eltiyeb Ali |
| collection | DOAJ |
| description | In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ2=φ, there exist an idempotent element e2=e such that φ = ce. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products. |
| first_indexed | 2024-03-09T03:01:47Z |
| format | Article |
| id | doaj.art-3d3ccd77b6c54713afcfe8b7187eb5f7 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-03-09T03:01:47Z |
| publishDate | 2023-10-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-3d3ccd77b6c54713afcfe8b7187eb5f72023-12-04T12:13:04ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392023-10-012110810810.28924/2291-8639-21-2023-1082333On Crossed Product Rings Over p.q.-Baer and Quasi-Baer RingsEltiyeb Ali0a:1:{s:5:"en_US";s:18:"NAJRAN University ";}In this paper, we consider a ring R and a monoid M equipped with a twisting map f: M×M -> U(R) and an action map ω: M -> Aut(R). The main objective of our study is to investigate the conditions under which the crossed product structure R⋊M is p.q.-Baer and quasi-Baer rings, and how this property relates to the p.q.-Baer property of R and the existence of a generalized join in I(R) for M-indexed subsets, where I(R) denotes the set of ideals of R. Additionally, we prove a connection between R being a left p.q.-Baer ring and the CM-quasi-Armendariz property. Moreover, we prove that for any element φ2=φ, there exist an idempotent element e2=e such that φ = ce. We then prove that R is quasi-Baer if and only if the crossed product structure R⋊M is quasi-Baer. Finally, we present novel results regarding various constructions for crossed products.http://etamaths.com/index.php/ijaa/article/view/2948 |
| spellingShingle | Eltiyeb Ali On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings International Journal of Analysis and Applications |
| title | On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings |
| title_full | On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings |
| title_fullStr | On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings |
| title_full_unstemmed | On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings |
| title_short | On Crossed Product Rings Over p.q.-Baer and Quasi-Baer Rings |
| title_sort | on crossed product rings over p q baer and quasi baer rings |
| url | http://etamaths.com/index.php/ijaa/article/view/2948 |
| work_keys_str_mv | AT eltiyebali oncrossedproductringsoverpqbaerandquasibaerrings |