Noncommutative unique factorization domain
Introduction 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''0 + ''a''1'''i''' + ''a''2'''j''' + ''a''3'''k''' is integral if either all the coefficients ''a''i are integers or all of them are half-integers. * All free associative algebras.
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,
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