Bulletin of the
Korean Mathematical Society BKMS

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