Let R be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly J-ideals as new generalization J-ideals. We call proper ideal I J-ideal if whenever a,b ? 0 ab and J(R), then b I. Many basic properties characterizations are studied. investigate under various contexts constructions such direct products, localizations, homomorphic images. Moreover, number exam...

Let $D$ be an integral domain and $\Gamma$ a torsion-free commutative cancellative (additive) semigroup with identity element quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[\Gamma]$ is weakly Krull only UMT-domain, UMT-monoid, $G$ of type $(0,0,0, \dots )$ except $p$). Moreover, give arithmetical applications result.