Sa-supplement submodules
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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.
Abstract
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.
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