---
tag: W493DD6DAT
kind: concept
name: Alternativity
aliases: [alternative-binary-operation, alternative-magma, alternative-operation, alternative-property, left-alternative, left-alternativity, right-alternative, right-alternativity]
sources:
  - wikipedia: en:186050@r1372817755
    locator: Alternativity
    note: adopted
    mention: wikipedia://en/186050
    sections: [Summary]
same_as:
  wikidata: Q438727
  wikipedia: Alternativity
inventory: [41WG3AS6WC]
---

## Summary

In abstract algebra, **alternativity** is a property of a [[binary operation|0580ZJSA3Q]]. A magma $G$ is said to be **left alternative** if $(xx)y = x(xy)$ for all $x, y \in G$ and **right alternative** if $y(xx) = (yx)x$ for all $x, y \in G$. A magma that is both left and right alternative is said to be **alternative**.