On σ-primeness and σ-semiprimeness in rings with involution
This study introduces the structure of $\left\vert\mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-semiprime ring, $\left\vert \mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-prime ring, and source of $\sigma$-primeness , which have not been previously explored, and presents new results. We define a s...
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| Format: | Article |
| Language: | English |
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Tokat Gaziosmanpasa University
2024-12-01
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| Series: | Journal of New Results in Science |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4347966 |
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| author | Barış Albayrak Didem Karalarlıoğlu Camcı Didem Yeşil |
| author_facet | Barış Albayrak Didem Karalarlıoğlu Camcı Didem Yeşil |
| author_sort | Barış Albayrak |
| collection | DOAJ |
| description | This study introduces the structure of $\left\vert\mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-semiprime ring, $\left\vert \mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-prime ring, and source of $\sigma$-primeness , which have not been previously explored, and presents new results. We define a subset $$P_{R_{\sigma}} = \bigcap_{a\in R} S_{R_{\sigma}}^{a}$$ of ring $R$ as $S_{R}^{\sigma}=\left\{ \left. a\in R\right\vert aRa=aR{\sigma}(a)=(0)\right\} $, where $\sigma$ is an involution is referred to as the source of $\sigma$-primeness of $R$. Additionally, we have established some relationships between the prime radical$\beta(R)$ and $\mathcal{S}_{R}^{\sigma}$. |
| format | Article |
| id | doaj-art-3eb8ec2fba8e448d8a9d68cdd3fde590 |
| institution | DOAJ |
| issn | 1304-7981 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Tokat Gaziosmanpasa University |
| record_format | Article |
| series | Journal of New Results in Science |
| spelling | doaj-art-3eb8ec2fba8e448d8a9d68cdd3fde5902025-08-20T02:41:08ZengTokat Gaziosmanpasa UniversityJournal of New Results in Science1304-79812024-12-0113326227010.54187/jnrs.1581184142On σ-primeness and σ-semiprimeness in rings with involutionBarış Albayrak0https://orcid.org/0000-0002-8255-4706Didem Karalarlıoğlu Camcı1https://orcid.org/0000-0002-8413-3753Didem Yeşil2https://orcid.org/0000-0003-0666-9410CANAKKALE ONSEKIZ MART UNIVERSITYCANAKKALE ONSEKIZ MART UNIVERSITYÇANAKKALE ONSEKİZ MART ÜNİVERSİTESİThis study introduces the structure of $\left\vert\mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-semiprime ring, $\left\vert \mathcal{S}_{R}^{\sigma}\right\vert $-$\sigma$-prime ring, and source of $\sigma$-primeness , which have not been previously explored, and presents new results. We define a subset $$P_{R_{\sigma}} = \bigcap_{a\in R} S_{R_{\sigma}}^{a}$$ of ring $R$ as $S_{R}^{\sigma}=\left\{ \left. a\in R\right\vert aRa=aR{\sigma}(a)=(0)\right\} $, where $\sigma$ is an involution is referred to as the source of $\sigma$-primeness of $R$. Additionally, we have established some relationships between the prime radical$\beta(R)$ and $\mathcal{S}_{R}^{\sigma}$.https://dergipark.org.tr/en/download/article-file/4347966involutionσ-prime ringσ-semiprime ringsource of primenesssource of semiprimeness |
| spellingShingle | Barış Albayrak Didem Karalarlıoğlu Camcı Didem Yeşil On σ-primeness and σ-semiprimeness in rings with involution Journal of New Results in Science involution σ-prime ring σ-semiprime ring source of primeness source of semiprimeness |
| title | On σ-primeness and σ-semiprimeness in rings with involution |
| title_full | On σ-primeness and σ-semiprimeness in rings with involution |
| title_fullStr | On σ-primeness and σ-semiprimeness in rings with involution |
| title_full_unstemmed | On σ-primeness and σ-semiprimeness in rings with involution |
| title_short | On σ-primeness and σ-semiprimeness in rings with involution |
| title_sort | on σ primeness and σ semiprimeness in rings with involution |
| topic | involution σ-prime ring σ-semiprime ring source of primeness source of semiprimeness |
| url | https://dergipark.org.tr/en/download/article-file/4347966 |
| work_keys_str_mv | AT barısalbayrak onsprimenessandssemiprimenessinringswithinvolution AT didemkaralarlıoglucamcı onsprimenessandssemiprimenessinringswithinvolution AT didemyesil onsprimenessandssemiprimenessinringswithinvolution |