Arep-Algebras Having Cyclic Quadratic Extensions Necessarily Cyclic?

Albertʹs candidate for a noncyclicp-algebra of prime degreepis actually seen to be ap-symbol (and thereby cyclic), as a consequence of calculations related to the corestriction down a quadratic extension. More generally, under many circumstances (which subsume the known casep = 3), ap-algebra of degreepwhich becomes cyclic after a quadratic extension of the center already is already cyclic. However, there is a proposed counterexample to this assertion in general, which may be noncyclic algebra forp ≥ 5.