Unifying strongly clean power series rings

Alexander J. Diesl, Daniel R. Shifflet
2018 Communications in Algebra  
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
more » ... 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.
doi:10.1080/00927872.2018.1444174 fatcat:pk5ilktcsvduzpbgkaat2bwyte