This paper is to study how to construct Frobenius pairs over a Morita ring [Formula: see text]. Given Frobenius pairs [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text], respectively, we construct Frobenius pairs [Formula: see text] and [Formula: see text] in [Formula: see text] under some conditions. As an application, we establish a sufficient and necessary condition of Gorenstein projective modules over the Morita ring [Formula: see text].
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Liang et al. (2024) studied this question.