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Characterization
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.