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 is termed power-associative if it satisfies the following equivalent conditions:
- The multiplicative magma of the ring is a power-associative magma.
- Every element of the ring is contained in an associative subring.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Associative ring||associativity holds universally||Alternative ring|FULL LIST, MORE INFO|
|Alternative ring||satisfies the alternative identities; associativity holds for subring generated by two elements|||FULL LIST, MORE INFO|
|Jordan ring||commutative, satisfies Jordan's identity|||FULL LIST, MORE INFO|