A Generalization of the Prime Radical of Rings

Year 2023, Volume: 6 Issue: 2 , 61 - 69 , 30.12.2023

Didem Karalarlıoğlu Camcı , Didem Yeşil , Rasie Mekera , Çetin Camcı

https://doi.org/10.38061/idunas.1401075

https://izlik.org/JA45FS22MX

Abstract

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.

Keywords

prime ring , prime ideal , prime radical , semiprime ideal

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