SA-SUPPLEMENT SUBMODULES

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 boolean AND T is semiartinian. The class of sa-supplement sequences 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 sasupplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.