Supercommutative algebra

A supercommutative algebra is a Z2 graded algebra such that for any two pure elements x,y of the algebra,

yx=(-1)xyxy

Equivalently, it is an algebra where the supercommutator

[x,y)≡xy-(-1)|x||y|yx

always vanishes.

Grassmann algebras are examples of a supercommutative algebra.

See also commutative algebra, Lie superalgebraTemplate:Math-stub

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