Noncommutative unique factorization domain

In mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property.

Examples

 * The ring of Hurwitz quaternions, also known as integral quaternions. A quaternion a = a0 + a1i + a2j + a3k is integral if either all the coefficients ai are integers or all of them are half-integers.


 * All free associative algebras.