Difference between revisions of "Ring"

 
Line 5: Line 5:
 
There exists an element, usually denoted 0, such that <math>0 + a = a + 0 = a</math> for all <math>a\in R</math>.
 
There exists an element, usually denoted 0, such that <math>0 + a = a + 0 = a</math> for all <math>a\in R</math>.
 
(List of other defining properties goes here.)
 
(List of other defining properties goes here.)
 +
 +
 +
Common examples of rings include the [[integer]]s or the integers taken [[modulo]] <math>n</math>, with addition and multiplication as usual.  In addition, every field is a ring.

Revision as of 13:23, 11 July 2006

This article is a stub. Help us out by expanding it.

A ring is a structure of abstract algebra, similar to a group or a field. A ring $R$ is a set of elements with two operations, usually called multiplication and addition and denoted $\cdot$ and $+$, which have the following properties:

There exists an element, usually denoted 0, such that $0 + a = a + 0 = a$ for all $a\in R$. (List of other defining properties goes here.)


Common examples of rings include the integers or the integers taken modulo $n$, with addition and multiplication as usual. In addition, every field is a ring.