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Abstract
A commutative ring R is said to be strongly Hopfian if the chain of annihilators ann(a) ⊆ ann(a 2) ⊆ … stabilizes for each a ∈ R. In this article, we are interested in the class of strongly Hopfian rings and the transfer of this property from a commutative ring R to the ring of the power series R[[X]]. We provide an example of a strongly Hopfian ring R such that R[[X]] is not strongly Hopfian. We give some necessary and sufficient conditions for R[[X]] to be strongly Hopfian.
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ACKNOWLEDGMENT
The author would like to thank Professor A. Kaidi for his inspiring suggestion on this work and for hospitality at Almeria University, Spain. She also thanks the referee for his/her careful considerations.
Notes
Communicated by I. Swanson.