We previously showed that the inverse limit of standard-graded polynomial rings with perfect (or semiperfect) coefficient field is a polynomial ring in an uncountable number of variables. In this paper, we show that the result holds with no hypothesis on the coefficient field. We also prove an analogous result for ultraproducts of polynomial rings.
"Big Polynomial Rings with Imperfect Coefficient Fields." Michigan Math. J. 70 (3) 649 - 672, August 2021. https://doi.org/10.1307/mmj/1603353740