2007/02/06 by Mimouni, Abdeslam
#13A15 #13F20 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0702142
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∩ R)[X] with Q∩ 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 Prüfer domain R for which the v-operation is not stable.