real ring

A ring A is called real iff the following identityPlanetmathPlanetmath holds for all n :

a12++an2=0a1,,an=0  (a1,,anA)

If A is a ring then being real implies the following

Conversely, we note that if A is reduced and can have a partial ordering then A is a real ring. If A is a field then we call it a real field. Similarly we define real domains, real (von Neumann) regular ringsMathworldPlanetmath,

Title real ring
Canonical name RealRing
Date of creation 2013-03-22 18:51:35
Last modified on 2013-03-22 18:51:35
Owner jocaps (12118)
Last modified by jocaps (12118)
Numerical id 6
Author jocaps (12118)
Entry type Definition
Classification msc 13J30
Classification msc 13J25
Related topic FormallyRealField