It is a major open problem (raised by Albert) whether every division algebra of prime degree over a field is cyclic. This is true if the degree is 2 or 3, but the problem is wide open for primes at least 5. The known results are only for special classes of fields. For example, if "K" is a global field or local field, then a division algebra of any degree over "K" is cyclic, by Albert–Brauer–Hasse–Noether. A "higher-dimensional" result in the same direction was proved by Saltman: if "K" is a field of transcendence degree 1 over the local field Q"p", then every division algebra of prime degree "l" ≠ "p" over "K" is cyclic.