Bull. Korean Math. Soc. 2013; 50(2): 459-467
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.459
Copyright © The Korean Mathematical Society.
Hangyu Yan
China Pharmaceutical University
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, $\Sigma$-pure injective
MSC numbers: 16D10, 16E30
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