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Embedding of modules over Noetherian rings

Chonghui Huang, Zhenghua Xu

Abstract


Let R and S be Noetherian rings. For any semidualizing bimodule RCS, we shows that the injective dimension of C as a right S-module is at most n if and only if every finitely generated R-module can be embedded into an R-module with C-flat dimension at most n. As an application, we prove that a commutative Noetherian ring R is Gorenstein with self-injective dimension at most n if and only if every finitely generated R-module can be embedded into a finitely generated R-module with projective dimension at most n. Some known results can be our corollaries.

Keywords


Semidualizing bimodule, Self-injective dimension, Gorenstein ring.

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