Right-alternative ring

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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


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:

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