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
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
|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|