# Associative

From Maths

Revision as of 07:44, 27 April 2015 by Alec (Talk | contribs) (Created page with " ==Definition== An operator is associative<ref>Algebra - Serge Lang - Revised Third Edition - GTM</ref> if: * <math>(xy)z=x(yz)</math> where {{M|xy}} denotes the operator acti...")

## Definition

An operator is associative^{[1]} if:

- [math](xy)z=x(yz)[/math] where [ilmath]xy[/ilmath] denotes the operator acting on [ilmath]x[/ilmath] and [ilmath]y[/ilmath]

In fact given a function [ilmath]\times:S\times S\rightarrow S[/ilmath] we even call the image of [ilmath](x,y)[/ilmath] under [ilmath]\times[/ilmath] the *product* (or indeed the *sum* if we're using additive notation)

## References

- ↑ Algebra - Serge Lang - Revised Third Edition - GTM