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 $n$-prime
radical 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.
Primary Language | English |
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Subjects | Algebra and Number Theory |
Journal Section | Articles |
Authors | |
Publication Date | December 30, 2023 |
Submission Date | December 6, 2023 |
Acceptance Date | December 18, 2023 |
Published in Issue | Year 2023 Volume: 6 Issue: 2 |