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 a_i are integers or all of them are half-integers.

• All free associative algebras.^[1]

References

• P.M. Cohn, "Noncommutative unique factorization domains", Transactions of the American Mathematical Society 109:2:313-331 (1963). full text
• R. Sivaramakrishnan, Certain number-theoretic episodes in algebra, CRC Press, 2006, ISBN 0-8247-5895-1