The Merkurjev–Suslin theorem in algebraic K-theory has a strong consequence about the Brauer group. Namely, for a positive integer "n", let "K" be a field in which "n" is invertible such that "K" contains a primitive "n"th root of unity. Then the subgroup of the Brauer group of "K" killed by "n" is generated by cyclic algebras of degree "n". Equivalently, any division algebra of period dividing "n" is Brauer equivalent to a tensor product of cyclic algebras of degree "n". Even for a prime number "p", there are examples showing that a division algebra of period "p" need not be actually isomorphic to a tensor product of cyclic algebras of degree "p".