Abstract:
A right R-module M is called uniserial if its submodules are linearly ordered by inclusion,
i.e., for any submodules A and B of M, either A⊆ B or B ⊆ A. A ring R is right uniserial if
it is uniserial as a right R-module. A right R-module M is called a serial module if it is a
direct sum of uniserial modules. A ring R is right serial if it is serial as a right R-module
and R is serial if R is left and right serial. Modifying some structures of uniserial and serial
rings over associative arbitrary rings, present study develops some properties of uniserial
and serial modules over associative endomorphism rings. Some characterizations of
Noetherian (resp. Artinian) uniserial and serial modules over endomorphism rings are also
investigated in the present study.
