• ${\displaystyle xy-(-1)^{|x||y|}yx}$
• ${\displaystyle x^{2}}$ when |x| is odd
for homogeneous elements x, y in M of degree |x|, |y|. By construction, a graded-symmetric algebra is graded-commutative; i.e., ${\displaystyle xy=(-1)^{|x||y|}yx}$ and is universal for this.