TY  - JOUR
T1  - A Generalization of the Prime Radical of Rings
AU  - Karalarlıoğlu Camcı, Didem
AU  - Yeşil, Didem
AU  - Mekera, Rasie
AU  - Camcı, Çetin
PY  - 2023
DA  - December
Y2  - 2023
DO  - 10.38061/idunas.1401075
JF  - Natural and Applied Sciences Journal
JO  - IDU Natural and Applied Sciences Journal (IDUNAS)
PB  - Izmir University of Democracy
WT  - DergiPark
SN  - 2645-9000
SP  - 61
EP  - 69
VL  - 6
IS  - 2
LA  - en
AB  - Let $R$ be a ring, $I$ be an ideal of $R$, and $\sqrt{I}$ be a prime radical of $I$. This study generalizes the prime radical of $\sqrt{I}$ where it denotes by $\sqrt[n+1]{I}$, for $n\in \mathbb{Z}^{+}$. This generalization is called $n$-primeradical of ideal $I$. Moreover, this paper shows that $R$ is isomorphic to a subdirect sum of ring $H_{i}$ where $%H_{i}$ are  $n$-prime rings. Furthermore, two open problems are presented.
KW  - prime ring
KW  - prime ideal
KW  - prime radical
KW  - semiprime ideal
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UR  - https://doi.org/10.38061/idunas.1401075
L1  - https://dergipark.org.tr/en/download/article-file/3582525
ER  -