Characterizations of Noetherian and hereditary rings

He, Zheng-Xu

doi:10.1090/S0002-9939-1985-0773992-0

Characterizations of Noetherian and hereditary rings
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Proc. Amer. Math. Soc. 93 (1985), 414-416 Request permission

Abstract:

We characterize the left Noetherian rings by the existence of decompositions of left modules into direct sums of an injective submodule and a submodule containing no injective submodule except 0. We also prove that a left Noetherian ring is left hereditary iff the suspension of each left ideal (see [7]) is injective or, equivalently, the above decomposition is unique.

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