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 . An ideal I is said to be a Ratliff–Rush ideal if
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.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
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.
Notes
Communicated by I. Swanson.