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Anticommutative algebra

In mathematics, a supercommutative (associative) algebra (sometimes termed a commutative superalgebra) is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elementsx, y we have yx=(−1)|x||y|xy,{\displaystyle yx=(-1)^{|x||y|}xy,}where |x| denotes the grade of the element and is 0 or 1 (in Z2) according to whether the grade is even or odd, respectively.

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