Right-alternative ring

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

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 $R$ (i.e., a not necessarily associative ring $R$) satisfying the following identity:

$x*(y*y)=(x*y)*y\ \forall x,y\in R$

where $*$ is the multiplication of $R$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Associative ring				|FULL LIST, MORE INFO
Alternative ring				|FULL LIST, MORE INFO