An extension of commutative rings with unity is called a root extension if for each element , there exists a positive integer such that . Unlike the integral extension, the root extension is not stable under polynomial ring extension. We characterize when the extension of polynomial rings is a root extension. Using the characterization, we can give a positive answer to the question posed by Anderson, Dumitrescu and Zafrullah (2004), i.e., being a root extension implies that is a root extension. We also characterize when the extension of power series rings is a root extension.
"Root extension in polynomial and power series rings." J. Commut. Algebra 13 (1) 129 - 136, Spring 2021. https://doi.org/10.1216/jca.2021.13.129