Abstract
This article 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 ≠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 Prufer domain R for which the v-operation is not stable.
| Original language | English |
|---|---|
| Pages (from-to) | 4249-4256 |
| Number of pages | 8 |
| Journal | Communications in Algebra |
| Volume | 36 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 2008 |
Bibliographical note
Funding Information:The author would like to express his sincere thanks to the referee for his/her suggestions and comments. This work is supported by KFUPM.
Keywords
- Ideal-Maximal
- Semistar operation
- Star operation
- UMT-domain
- Upper to zero
ASJC Scopus subject areas
- Algebra and Number Theory