Difference between revisions of "Left alternative magma"
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Latest revision as of 23:15, 5 March 2010
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 leftalternative magma if it satisfies the following identity:
.
Relation with other properties
Property obtained by the opposite operation
If is a magma and we define on by , then is a leftalternative magma if and only if is a rightalternative magma.
Stronger properties
Property  Meaning  Proof of implication  Proof of strictness (reverse implication failure)  Intermediate notions 

Alternative magma  both left and rightalternative  FULL LIST, MORE INFO  
Semigroup  associativity holds universally  Alternative magma, Diassociative magmaFULL LIST, MORE INFO  
Diassociative magma  submagma generated by any two elements is associative  Alternative magmaFULL LIST, MORE INFO 
Weaker properties
Property  Meaning  Proof of implication  Proof of strictness (reverse implication failure)  Intermediate notions 

Magma in which cubes are welldefined  every element commutes with its square  FULL LIST, MORE INFO 
Incomparable properties
Property  Meaning  Proof of one nonimplication  Proof of other nonimplication  Notions stronger than both  Notions weaker than both 

Flexible magma  Diassociative magma, Left Bol magma with neutral elementFULL LIST, MORE INFO  Magma in which cubes are welldefinedFULL LIST, MORE INFO  
Rightalternative magma  Alternative magma, Diassociative magmaFULL LIST, MORE INFO  Magma in which cubes are welldefinedFULL LIST, MORE INFO  
Powerassociative magma  all powers are welldefined  Diassociative magmaFULL LIST, MORE INFO  Magma in which cubes are welldefinedFULL LIST, MORE INFO 