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.