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MATLIS INJECTIVE MODULES

  • Yan, Hangyu
  • Received : 2011.10.15
  • Published : 2013.03.31

Abstract

In this paper, Matlis injective modules are introduced and studied. It is shown that every R-module has a (special) Matlis injective preenvelope over any ring R and every right R-module has a Matlis injective envelope when R is a right Noetherian ring. Moreover, it is shown that every right R-module has an ${\mathcal{F}}^{{\perp}1}$-envelope when R is a right Noetherian ring and $\mathcal{F}$ is a class of injective right R-modules.

Keywords

Matlis injective module;(pre)envelope;${\sum}$-pure injective

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Cited by

  1. Relative Projective and Injective Dimensions vol.44, pp.8, 2016, https://doi.org/10.1080/00927872.2015.1065852
  2. Matlis flat modules vol.9, pp.2, 2016, https://doi.org/10.1515/tmj-2016-0023

Acknowledgement

Supported by : China Pharmaceutical University