Bulletin of the
Korean Mathematical Society BKMS

In this paper, the notions of $iw$-split modules and $iw$-split dimension are introduced, and some equivalent characterizations of these notions are given. With the help of $iw$-split modules and $iw$-split dimensions, new characterizations of DW rings, semi-simple rings, and Dedekind domains are given. More precisely, it is shown that $R$ is a DW ring if and only if every $iw$-split module is an injective module; while $R$ is a semi-simple ring if and only if every $R$-module is an $iw$-split module; and $R$ is a Dedekind domain if and only if every factor module of an $iw$-split module is $iw$-split.

Keywords: $w$-split module, $iw$-split module, $iw$-split dimension, Dedekind domain

MSC numbers: 13D05, 13D07, 13F05

Supported by: This work was supported by the Foundation of Chengdu University of Information Technology (KYTZ2022147).