Opposite magma

Definition

Suppose $(S,*)$ is a magma, i.e., $S$ is a set and $*$ is a binary operation on $S$. The opposite magma denoted $S^{op}$, is the magma $(S,\cdot )$, where:

$\!a\cdot b:=b*a$

Here, $\cdot$ is termed the opposite binary operation to $*$.

Related properties

• Self-opposite magma is a magma that is isomorphic to its opposite magma.
• Magma isotopic to its opposite magma is a magma that is isotopic to its opposite magma.
• Commutative magma is a magma that is equal to its opposite magma, in the sense that the binary operation and the opposite binary operation coincide.
• Involutive magma is a magma for which there exists a permutation of order two on the set that gives an isomorphism between the magma structure and the opposite magma structure.