Note on the star operations over polynomial rings

Abstract

This paper studies the notions of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in $R[X]$ is a $\ast$-maximal ideal and when a $\ast$-maximal ideal $Q$ of $R[X]$ is extended from $R$, that is, $Q=(Q\cap R)[X]$ with $Q\cap R\ne 0$, for a given star operation of finite character $\ast$ on $R[X]$. We also answer negatively some questions raised by Anderson-Clarke by constructing a Prüfer domain $R$ for which the $v$-operation is not stable.

9 pages

Cited by in corpus (1)

• On $v$--domains and star operations