Kummer Spaces in Cyclic Algebras of Prime Degree
  We classify the monomial Kummer subspaces of division cyclic 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 cyclic algebra, the dimension of any Kummer subspace is at most $p+1$. 
Adam Chapman, David J. Grynkiewicz, Eliyahu Matzri, Louis H. Rowen,   Uzi Vishne
math.RA