A Generalization of the Prime Radical of Rings

Authors : Didem Karalarlioğlu Camci, Didem Yeşil, Rasie Mekera, Çetin Camci

Pages : 61-69

Doi:10.38061/idunas.1401075

View : 49 | Download : 84

Publication Date : 2023-12-30

Article Type : Research Paper

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