Sa-supplement submodules
Bull. Korean Math. Soc. 2021 Vol. 58, No. 1, 147-161
https://doi.org/10.4134/BKMS.b200128
Published online November 3, 2020
Printed January 31, 2021
Y{\i}lmaz Dur\u{g}un
\c{C}ukurova University
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.
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)
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