# Right-alternative ring

From Groupprops

This article defines a non-associative ring property: a property that an be evaluated to true or false for any non-associative ring.

View other non-associative ring properties

## Contents

## Definition

### Symbol-free definition

A non-associative ring (i.e., a not necessarily associative ring) is termed a **right-alternative ring** if it satisfies the following equivalent conditions:

- The associator function is an alternating function of its middle and right variable.
- The multiplicative magma of the ring is a right-alternative magma.

### Definition with symbols

A **right-alternative ring** is a non-associative ring (i.e., a not necessarily associative ring ) satisfying the following identity:

where is the multiplication of .

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Associative ring | Alternative ring|FULL LIST, MORE INFO | |||

Alternative ring | |FULL LIST, MORE INFO |