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 [DDGK12] and [DDI+13]. 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.
Diesl, Alexander J. and Shifflet, Daniel R., "Unifying Strongly Clean Power Series Rings" (2018). Faculty Research and Scholarship. 169.