Goldie absolute direct summand rings and modules

Truong Cong Quynh, Serap Sahinkaya, Department of Mathematics, Danang University, 459 Ton Duc Thang, DaNang city, Vietnam, e-mail: tcquynh@dce.udn.vn", Department of Mathematics, Faculty of Science, Gebze Technical University, Kocaeli, Turkey, e-mail: srpsahinkaya@gmail.com
2018 Studia Universitatis Babes-Bolyai Matematica  
In the present paper, we introduce and study Goldie ADS modules and rings, which subsume two generalizations of Goldie extending modules due to Akalan et al. [3] and ADS-modules due to Alahmadi et al. [7]. A module M will be called a Goldie ADS module if for every decomposition M = S ⊕ T of M and every complement T of S, there exists a submodule D of M such that T βD and M = S ⊕ D. Various properties concerning direct sums of Goldie ADS modules are established. Mathematics Subject
more » ... bject Classification (2010): 16D40, 16E50, 16N20.
doi:10.24193/subbmath.2018.4.02 fatcat:bbrs357dnbglnoocl4vdududpm