Mathematics – Commutative Algebra
Scientific paper
2007-02-06
Mathematics
Commutative Algebra
9 pages
Scientific paper
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 $*$-maximal ideal and when a $*$-maximal ideal $Q$ of $R[X]$ is extended from $R$, that is, $Q=(Q\cap R)[X]$ with $Q\cap R\not =0$, for a given star operation of finite character $*$ on $R[X]$. We also answer negatively some questions raised by Anderson-Clarke by constructing a Pr\"ufer domain $R$ for which the $v$-operation is not stable.
No associations
LandOfFree
Note on the star operations over polynomial rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Note on the star operations over polynomial rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Note on the star operations over polynomial rings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-427392