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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Supported by the NSF of China (No. 11371131) and the Construct Program of the Key Discipline in Hunan Province.
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Li, W., Ouyang, B. (n, d)-Injective covers, n-coherent rings, and (n, d)-rings. Czech Math J 64, 289–304 (2014). https://doi.org/10.1007/s10587-014-0101-1
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DOI: https://doi.org/10.1007/s10587-014-0101-1