Definition:Principal Ideal of Ring/Notation

Principal Ideal of Ring: Notation

From Principal Ideal of Commutative Ring the notions of principal left ideal, principal right ideal and principal ideal coincide.

So often, in some sources, a principal ideal of a commutative ring with unity is denoted as $a R$.

This is done most often in the case where it is important to identify the ring that the principal ideal belongs to.

The notation $a R$ is often used when the ring $R$ in question is the integers $\Z$ or the $p$-adic integers $\Z_p$.

So it is common for $n \Z$ to denote the principal ideal of $\Z$ generated by $n$ and $p^k\Z_p$ to denote the principal ideal of $\Z_p$ generated by $p^k$.