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Flexible magma

This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.
View other such properties
This is a variation of semigroup|Find other variations of semigroup |

Contents

Definition

A magma (S,*) is termed a flexible magma if it satisfies the following identity:

x * (y * x) = (x * y) * x \ \forall \ x,y \in S.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Diassociative magma submagma generated by any two elements is associative |FULL LIST, MORE INFO
Semigroup Associativity holds universally Diassociative magma|FULL LIST, MORE INFO
Commutative magma Commutativity holds universally |FULL LIST, MORE INFO
Flexible loop loop that is flexible as a magma |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Magma in which cubes are well-defined every element commutes with its square Magma in which cubes are well-defined and every element commutes with its cube|FULL LIST, MORE INFO