my-server
← Wiki

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 = a<sub>0</sub> + a<sub>1</sub>i + a<sub>2</sub>j + a<sub>3</sub>k is integral if either all the coefficients a<sub>i</sub> are integers or all of them are half-integers.

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,

Notes