Bulletin of the
Korean Mathematical Society BKMS

In this paper, we introduced and studied sa-supplement submodules. A submodule $U$ of a module $V$ is called an sa-supplement submodule in $V$ if there exists a submodule $T$ of $V$ such that $V=T+U$ and $U\cap T$ is semiartinian. The class of sa-supplement sequences $\mathcal{SAS}$ is a proper class which is generated by socle-free modules injectively. We studied modules that have an sa-supplement in every extension, modules whose all submodules are sa-supplement and modules whose all sa-supplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.

Keywords: Proper class of short exact sequences, sa-supplement submodule, sa-supplementing modules, semiartinian modules

MSC numbers: Primary 16D10, 18G25

Supported by: This work was financially supported by the Scientific and Technological Research Council of Turkey (TUBITAK) (Project number: 119F176)