Kummer spaces in symbol algebras of prime degree
We classify the monomial Kummer subspaces of division symbol algebras of prime degree p, showing that every such space is standard, and in particular the dimension is no greater than p+ 1. It follows that in a generic symbol algebra, the dimension of any Kummer subspace is at most p+ 1.
Journal of Pure and Applied Algebra
Chapman, A., Grynkiewicz, D., Matzri, E., Rowen, L., & Vishne, U. (2016). Kummer spaces in symbol algebras of prime degree. Journal of Pure and Applied Algebra, 220 (10), 3363-3371. https://doi.org/10.1016/j.jpaa.2016.04.003