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

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

(2) The  (a,b)(c,d)=(ac,bd,(a+b)(c+d))  for multiplying ideals of R is valid always when at least one of the elements a, b, c, d of R is not zero-divisor.

(3) Every overring of R is integrally closedMathworldPlanetmath.

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

Title characterisation
Canonical name Characterisation
Date of creation 2013-03-22 14:22:28
Last modified on 2013-03-22 14:22:28
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 18
Author pahio (2872)
Entry type Definition
Classification msc 00A05
Synonym characterization
Synonym defining property
Related topic AlternativeDefinitionOfGroup
Related topic EquivalentFormulationsForContinuity
Related topic MultiplicationRuleGivesInverseIdeal