User:CJKG/Eigenbox

a) ${\mathcal {M}}$ is called right-equiponent magma or R-equiponent magma if and only if $\exists M,\circ$ with $((M;\circ )={\mathcal {M}}\wedge \circ :M\times M\to M)$ such that $\forall a\in M\exists b\in M\forall c\in M(c\circ a)\circ c=b$ (R-equiponency law).

b) ${\mathcal {M}}$ is called left-equiponent magma or L-equiponent magma if and only if $\exists M,\circ$ with $((M;\circ )={\mathcal {M}}\wedge \circ :M\times M\to M)$ such that $\forall a\in M\exists b\in M\forall c\in Mc\circ (a\circ c)=b$ (L-equiponency law).

Remark: $M=\emptyset$ is allowed.