ABSTRACT
It is unknown whether a power series ring over a strongly clean ring is, itself, always strongly clean. Although a number of authors have shown that the above statement is true in certain special cases, the problem remains open, in general. In this article, we look at a class of strongly clean rings, which we call the optimally clean rings, over which power series are strongly clean. This condition is motivated by work in [Citation10] and [Citation11]. We explore the properties of optimally clean rings and provide many examples, highlighting the role that this new class of rings plays in investigating the question of strongly clean power series.
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Acknowledgments
The authors would like to thank Dr. Warren Wm. McGovern for his time and assistance in completing this paper. The authors would also like to give a hearty thanks to the anonymous referee, whose careful reading and thoughtful suggestions were most appreciated.