Divisibility-preserving function
From Number
Template:Arithmetic function property
Definition
Suppose is an arithmetic function, i.e.,
is a function from the natural numbers to a commutative unital ring
. We say that
is divisibility-preserving if, whenever
and
are natural numbers such that
divides
,
divides
.
Note that whether a function is divisibility-preserving depends on what we consider the target ring.