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In mathematics, a supercommutative algebra is a superalgebra such that for any two homogeneous elements x, y we have

where |x| denotes the grade of the element and is 0 or 1 according to whether the grade is even or odd, respectively.

Equivalently, it is a superalgebra where the supercommutator

always vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as skew-commutative associative algebras to emphasize the anti-commutation, or, to emphasize the grading, graded-commutative or, if the supercommutativity is understood, simply commutative.

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