Abstract
We characterize, in terms of properties of homogeneous elements, when a graded domain is pre-Schreier or Schreier. As a consequence, the following properties of a commutative monoid domain A [ M ] are equivalent: (1) A [ M ] is pre-Schreier; (2) A [ M ] is Schreier; (3) A and M are Schreier. This is in contrast to pre-Schreier monoids and pre-Schreier integral domains, which need not be Schreier.
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