TY  - JOUR
T1  - On σ-primeness and σ-semiprimeness in rings with involution
AU  - Yeşil, Didem
AU  - Karalarlıoğlu Camcı, Didem
AU  - Albayrak, Barış
PY  - 2024
DA  - December
Y2  - 2024
DO  - 10.54187/jnrs.1581184
JF  - Journal of New Results in Science
JO  - JNRS
PB  - Tokat Gaziosmanpasa University
WT  - DergiPark
SN  - 1304-7981
SP  - 262
EP  - 270
VL  - 13
IS  - 3
LA  - en
AB  - 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 $\mathcal{S}_{R}^{\sigma}$.
KW  - Involution
KW  - σ-Prime ring
KW  - σ-Semiprime ring
KW  - Source of primeness
KW  - Source of semiprimeness
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UR  - https://doi.org/10.54187/jnrs.1581184
L1  - https://dergipark.org.tr/en/download/article-file/4347966
ER  -