Abstract
Let [Formula: see text] be an extension of integral domains and [Formula: see text] a commutative, additive, cancellative torsion-free monoid. Let [Formula: see text] be the semigroup ring of [Formula: see text] over [Formula: see text] and set [Formula: see text]. Suppose that [Formula: see text]. Then [Formula: see text] is a subring of [Formula: see text]. In this paper, we study primal elements in [Formula: see text] domains. As an application, we characterize when the construction [Formula: see text] is a (pre-)Schreier domain.
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