Cyclic module

In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is analogous to cyclic group, that is, a group that is generated by one element.
Definition.
A left "R"-module "M" is called cyclic if "M" can be generated by a single element i.e. for some "x" in "M". Similarly, a right "R"-module "N" is cyclic if for some .