Example

(1) Every monogenous group, being commutative (I, § 4, no. 10, Proposition 18), is a monogenous $\mathbf{Z}$-module. (2) If A is a commutative ring, the monogenous submodules of the A-module A are just the principal ideals (I, § 8, no. 6) of the ring A. (3) Every simple A-module E is monogenous, since the submodule of E generated by an element ≠ 0 of E is necessarily equal to E.