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This research investigates the weakly Gorenstein properties of tensor and Morita algebras.

December 22, 2025Open Access

Weakly Gorensteinness of tensor algebras and Morita algebras

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This research investigates the weakly Gorenstein properties of tensor and Morita algebras.
Analyzed left weakly Gorenstein conditions for tensor algebras where gl.dim B < ∞.
Computed and described (semi-)Gorenstein-projective left modules for a class of Morita algebras.
Utilized the monomorphism category method to establish results.
Demonstrated that a tensor algebra is left weakly Gorenstein if and only if its base algebra is.
Characterized (semi-)Gorenstein-projective modules for specific Morita algebras.
Showed that the upper triangular matrix algebra is left weakly Gorenstein if its components are.

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The paper demonstrates that tensor algebras are left weakly Gorenstein if their components are, implying implications for Morita algebras.

Gao et al. (2025) studied this question.

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The paper demonstrates that tensor algebras are left weakly Gorenstein if their components are, implying implications for Morita algebras.