Sa-Supplement Submodules
Bull. Korean Math. Soc.
Published online November 3, 2020
yılmaz DURGUN
Cukurova University
Abstract : In this paper, we introduced and studied sa-supplement submodules. A submodule U of a module V is called sa-supplement submodule in V if there exists a submodule T of V such that V=T+U and the intersection of U and 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 a 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, sa-supplement submodule, sa-supplementing modules, semiartinian modules
MSC numbers : 16D10, 16D50
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