We study certain properties of Noetherian rings with weak normality and seminormality in mixed characteristic. It is known that the two concepts can differ in the equal prime characteristic case, while they coincide by definition in the equal characteristic zero case. We exhibit some examples in the mixed characteristic case. We also establish the local Bertini theorem for weak normality in mixed characteristic under a certain condition.
Jun Horiuchi. Kazuma Shimomoto. "Weak normality and seminormality in the mixed characteristic case." J. Commut. Algebra 14 (3) 351 - 363, Fall 2022. https://doi.org/10.1216/jca.2022.14.351