Abstract
Let R be a commutative ring with unity. A proper ideal P of R is called -weakly prime
if
implies
for some
where
In 2014, Ebrahimpour [On generalizations of prime ideals (II). Comm. Algebra 42:3861–3875] posed two conjectures on
-weakly prime ideals. In this paper, we prove them.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgements
The authors express their deep gratitude to the referee for his/her meticulous reading and valuable suggestions which have definitely improved the paper.