Jordan magma
From Groupprops
This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.
View other such properties
Contents
Definition
A magma is termed a Jordan magma if it satisfies the following two conditions:
- Commutativity:
.
- Jordan's identity:
.
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
Abelian semigroup | ||||
Abelian group |
Weaker properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
Commutative magma | any two elements commute | (by definition) | |FULL LIST, MORE INFO | |
Flexible magma | ![]() |
(via commutativity) | Commutative magma|FULL LIST, MORE INFO | |
Magma in which cubes are well-defined | ![]() |
(via commutativity, flexibility) | Commutative magma, Magma in which cubes and fourth powers are well-defined, Magma in which powers up to the fifth are well-defined|FULL LIST, MORE INFO | |
Magma in which cubes and fourth powers are well-defined | ![]() ![]() |
Magma in which powers up to the fifth are well-defined|FULL LIST, MORE INFO | ||
Magma in which powers up to the fifth are well-defined | ![]() |
|FULL LIST, MORE INFO |