An easy example of 3-commutative algebra is $T_3(F)$, the algebra of all strictly upper triangular 3-by-3 matrices.

Another class of examples is given by the quandle algebras $F[X]$, where $X$ is a trivial quandle with more than one element.

An easy example of 3-commutative algebra is $T_3(F)$, the algebra of all strictly upper triangular 3-by-3 matrices.

Another class of examples is given by the quandle rings $F[X]$, where $F$ is a field and $X$ a trivial quandle with more than one element.

An easy example of 3-commutative algebra is $T_3(F)$, the algebra of all strictly upper triangular 3-by-3 matrices.

An easy example of 3-commutative algebra is $T_3(F)$, the algebra of all strictly upper triangular 3-by-3 matrices.

Another class of examples is given by the quandle algebras $F[X]$, where $X$ is a trivial quandle with more than one element.