Abstract.
The present paper is devoted to the study of those rings R such that for any ring homomorphism \(R\rightarrow S\) the functor ${\rm Hom}_R(S,-):R{\rm -Mod} \rightarrow S{\rm -Mod}$ preserves injective envelopes or injective covers.¶The case of injective envelopes has been studied by T. Würfel ([9]), who gave a characterization of such rings (Theorem 10). In this paper we give another characterization of those rings in Section 2. One of the tools we use is a generalization of a certain type of module initially studied by Northcott ([4]), McKerrow ([3]) and Park ([5] and [6]).¶The case of injective covers is treated in Section 3, where we give a complete characterization of commutative noetherian rings satisfying the property mentioned above.
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Received: 4.10.1999
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Dempsey, D., Oyonarte, L. & Song, YM. Ring extensions, injective covers and envelopes. Arch. Math. 76, 250–258 (2001). https://doi.org/10.1007/s000130050566
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DOI: https://doi.org/10.1007/s000130050566