Editing Superalgebra (section)

===Supercommutativity===

The '''[[supercommutator]]''' on ''A'' is the binary operator given by
:<math>[x,y] = xy - (-1)^{|x||y|}yx</math>
on homogeneous elements, extended to all of ''A'' by linearity. Elements ''x'' and ''y'' of ''A'' are said to '''supercommute''' if {{nowrap|1=[''x'', ''y''] = 0}}.

The '''supercenter''' of ''A'' is the set of all elements of ''A'' which supercommute with all elements of ''A'':
:<math>\mathrm{Z}(A) = \{a\in A : [a,x]=0 \text{ for all } x\in A\}.</math>
The supercenter of ''A'' is, in general, different than the [[center of an algebra|center]] of ''A'' as an ungraded algebra. A commutative superalgebra is one whose supercenter is all of ''A''.