Sa-supplement submodules
Bull. Korean Math. Soc. 2021 Vol. 58, No. 1, 147-161
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)
Downloads: Full-text PDF   Full-text HTML


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail:   | Powered by INFOrang Co., Ltd