Power-associative 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
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
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Associative ring | associativity holds universally | |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 |