In mathematics, characterisation usually means a property or a condition to define a certain notion. A notion may, under some presumptions, have different equivalent ways to define it.

For example, let be a commutative ring with non-zero unity (the presumption). Then the following are equivalent:

(1) All finitely generated regular ideals of are invertible.

(2) The formula for multiplying ideals of is valid always when at least one of the elements , , , of is not zero-divisor.

(3) Every overring of is integrally closed.

Each of these conditions is sufficient (and necessary) for characterising and defining the Prüfer ring.