Let $a$ and $b$ be elements of a commutative ring with non-zero unity and let $a \mid b$ If there is a positive integer $n$ such that $a^n \mid b$ , and $a^{n+1} \nmid b$ then $b$ is strictly divisible by $a^n$ this may be denoted by $$a^n \parallel b.$$ For example, $10^4 \parallel 520000$

Note. The expression ``strictly divisible'' may be used of course in a divisor monoid, too.