Akademik Veri Yönetim Sistemi
CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.2026, ss.1-15, 2026 (SCI-Expanded, Scopus)
Let $R$ be a commutative ring with identity, and $J(R)$ denote the Jacobson radical of $R$. This paper introduces $J$-prime ideals, generalizing prime ideals, $n$-ideals, and $J$-ideals. A proper ideal $I$ of $R$ is a $J$-prime ideal if for every $a, b \in R$, $ab \in I$ implies $a\in I+J(R) $ or $b \in I$. We characterize rings in which every proper ideal is $J$-prime, showing that a ring has the property that every proper ideal is $J$-prime if and only if it is a quasi-local ring. Also, we show that (0) is a $J$-prime ideal if and only if the ring is présimplifiable. Furthermore, we examine $J$-prime ideal characteristics in various ring constructions, such as homomorphic image of rings, quotient rings, cartesian product rings, polynomial rings, power series rings, trivial ring extension and amalgamation rings.