In abstract algebra, a Schreier domain, named after Otto Schreier, is an integrally closed domain where every nonzero element is primal; i.e., whenever x divides yz, x can be written as x = x1 x2 so that x1 divides y and x2 divides z.
An integral domain is said to be pre-Schreier if every nonzero element is primal.
The term "Schreier domain" was introduced by P. M. Cohn in 1960s.
The term "pre-Schreier domain" is due to Muhammad Zafrullah.
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