Power-associative 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

Definition

A non-associative ring is termed power-associative if it satisfies the following equivalent conditions:

  1. The multiplicative magma of the ring is a power-associative magma.
  2. 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 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