Covers and Envelopes by Submodules or Quotient-Modules

Yuedi Zeng and Faranak Farshadifar

Journal of Mathematics, 2023, vol. 2023, 1-9

Abstract: Let R be a ring, X a class of left R-modules, S the class of submodules of X, and Q the class of quotient-modules of X. It is shown that SQ is precovering (preenveloping) if and only if every injective (projective) left R-module has an X-precover (X-preenvelope). Both epic and monic S-(pre) covers (Q-(pre) envelopes) are studied. Moreover, some applications are given. In particular, it is proven that the injective envelope of any projective left R-module is projective if and only if the class of quotient-modules of projective and injective left R-modules is monic preenveloping.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9740245

DOI: 10.1155/2023/9740245

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