Title of article :
δ-Hollow Modules
Author/Authors :
hadi, inaam m. a. university of baghdad - college of education for pure science, (ibn al-haitham) - department of mathematics, Iraq , aidi, sameeah hasoon university of baghdad - college of education for pure science, (ibn al-haitham) - department of mathematics, Iraq
Abstract :
Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is
called a hollow module if every proper submodule N of M is small (N ≪ M), i.e. N + W ≠ M
for every proper submodule W in M. A δ-hollow module is a generalization of hollow
module, where an R-module M is called δ-hollow module if every proper submodule N of M
is δ-small (N δ
M), i.e. N + W ≠ M for every proper submodule W in M with M
W is singular.
In this work we study this class of modules and give several fundamental properties related
with this concept.
Keywords :
nonsingular module , singular module , δ-hollow module , hollow module , δ-small submodule , Small submodule
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
