Abstract
This article studies the Ratliff-Rush closure of an ideal in pullbacks and polynomial rings. By definition, the Ratliff-Rush closure of an ideal I of a domain R is the ideal given by Ĩ:=∪(In+1:RIn). An ideal I is said to be a Ratliff-Rush ideal if Ĩ=I and a domain R is a Ratliff-Rush domain if each ideal of R is a Ratliff-Rush ideal. We completely characterize pullbacks and polynomial rings such that every ideal is a Ratliff-Rush ideal.
| Original language | English |
|---|---|
| Pages (from-to) | 3044-3053 |
| Number of pages | 10 |
| Journal | Communications in Algebra |
| Volume | 37 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2009 |
Bibliographical note
Funding Information:I would like to express my sincere thanks to the referee for his/her helpful suggestions and comments. This work was funded by KFUPM under Project # FT070001.
Keywords
- Polynomial ring
- Pullback
- Ratliff-Rush closure
- Ratliff-Rush domain
- Ratliff-Rush ideal
ASJC Scopus subject areas
- Algebra and Number Theory