Let $R$ be a right and left principal ideal domain. An element $a\in R$ is said to be a right divisor of $b\in R$ if there exists $x \in R$ such that $xa=b$ . And similarly define left divisor.
$a$ is said to be a total divisor of $b$ if $RbR = <a>_R \cap$ $ _R<a>$ .
How do I prove the following theorem:
If $RbR \subseteq aR$ then $a$ is already a total divisor of $b$.
Thanks in advance.
I am finding pretty difficult to understand things in the noncommutative case.