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This analysis demonstrates how Frobenius pairs can be constructed in trivial ring extensions, suggesting implications for Morita rings.
Let [Formula: see text] be a trivial extension of a ring [Formula: see text] by an [Formula: see text]-[Formula: see text]-bimodule [Formula: see text]. We investigate how to construct Frobenius pairs (resp., strong Frobenius pairs) over [Formula: see text] by using Frobenius pairs (resp., strong Frobenius pairs) over [Formula: see text]. As an application, we apply some of our results to Morita rings with zero bimodule homomorphisms.
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Deng et al. (2025) studied this question.
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