J-IDEALS OF COMMUTATIVE RINGS

Let $R$ be a commutative ring with identity and $N(R)$ and
 $J\left(R\right)$ denote the nilradical Jacobson radical
 of $R$, respectively. A proper ideal $I$ is called an
 n-ideal if for every $a,b\in R$, whenever $ab\in I$\ $a\notin
 N(R)$, then $b\in I$. In this paper, we introduce study
 J-ideals as new generalization n-ideals in rings.
 $I$\ $R$\ J-ideal $ab\in
 $a\notin J\left(R\right) $, every
 R$. We study many properties examples such class of
 ideals. Moreover, investigate its relation some other
 classes ideals r-ideals, prime, primary maximal
 Finally, we, more generally, define J-submodules
 an $R$-modules $M$. clarify their properties
 especially case multiplication modules.