(n,d)-Injective covers,n-coherent rings,and (n,d)-rings |
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Authors: | Weiqing Li Baiyu Ouyang |
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Institution: | 1. College of Mathematics and Computer Science, Key Laboratory of High, Performance Computing and Stochastic Information Processing, (Ministry of Education of China), Hunan Normal University, Changsha, Hunan, 410 081, P.R. China
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Abstract: | It is known that a ring R is left Noetherian if and only if every left R-module has an injective (pre)cover. We show that (1) if R is a right n-coherent ring, then every right R-module has an (n, d)-injective (pre)cover; (2) if R is a ring such that every (n, 0)-injective right R-module is n-pure extending, and if every right R-module has an (n, 0)-injective cover, then R is right n-coherent. As applications of these results, we give some characterizations of (n, d)-rings, von Neumann regular rings and semisimple rings. |
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