characterisation
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 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 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.
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 |