On σ-primeness and σ-semiprimeness in rings with involution
Abstract
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 $\mathcal{S}_{R}^{\sigma}$.
Keywords
Involution, σ-Prime ring, σ-Semiprime ring, Source of primeness, Source of semiprimeness
Project Number
FBA-2019-2812
Thanks
The research has been supported by Çanakkale Onsekiz Mart University The Scientific Research Coordination Unit, Grant number: FBA-2019-2812.
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