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 flexible ring is a non-associative ring (i.e., a not necessarily associative ring) satisfying the following equivalent conditions:
- Its multiplication gives a flexible magma.
- The associator function is alternating in its first (i.e., leftmost) and third (i.e., rightmost) variable.
Definition with symbols
A flexible ring is a non-associative ring (i.e., a not necessarily associative ring) satisfying:
where is the multiplication in .
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Associative ring||ring in the usual sense, with associativity|
|Alternative ring||possibly nonassociative ring satisfying the alternative laws|
|Jordan ring||ring that is multiplicatively a Jordan magma|