Dergiler / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 1

?-supplemented modules relative to an ideal

?-supplemented modules relative to an ideal

Ali Reza Moniri HAMZEKOLAEE, Yahya TALEBİ, Rachid TRİBAK, Samira ASGARİ

Sayfa
107–120
DOI
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Abstract

Let I be an ideal of a ring R and let M be a left R-module. A submodule L ofM is said to be ?-small in M provided M 6= L + X for any proper submoduleX of M with M/X singular. An R-module M is called I-?-supplemented iffor every submodule N of M , there exists a direct summand K of M such thatM = N + K, N ? K ? IK and N ? K is ?-small in K. In this paper, weinvestigate some properties of I-?-supplemented modules. We also compareI-?-supplemented modules with ?-supplemented modules. The structure ofI-?-supplemented modules and ?-?-supplemented modules over a Dedekinddomain is completely determined.