(Hungerford exercise 31, page 143)

Let R be a commutative ring without identity and let $\displaystyle a \in R $

Show that $\displaystyle A = \{ ra + na \ | \ r \in R, n \in \mathbb{Z} \} $ is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)