Minimal prime ideals and semistar operations

چکیده مقاله

Let $R$ be a commutative integral domain and let $\star$ be a
semistar operation of finite type on $R$, and $I$ be a
quasi-$\star$-ideal of $R$. We show that, if every minimal prime
ideal of $I$ is the radical of a $\star$-finite ideal, then the set
$\Min(I)$ of minimal prime ideals over $I$ is finite.