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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Tokat Gaziosmanpasa University
2024-12-01
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| Series: | Journal of New Results in Science |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/4347966 |
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| Summary: | 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 $\mathcal{S}_{R}^{\sigma}$. |
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| ISSN: | 1304-7981 |