Let R be a 2-graded ringMathworldPlanetmath (or more generally, an associative algebra). We say that R is supercommutative if for any homogeneous elements a and bR:


In other words, even homogeneous elements are in the center of the ring, and odd homogeneous elements anti-commute.

Common examples of supercommutative rings are the exterior algebraMathworldPlanetmath of a module over a commutative ring (in particular, a vector spaceMathworldPlanetmath) and the cohomology ring of a topological space (both with the standard grading by degree reduced mod 2).

Title supercommutative
Canonical name Supercommutative
Date of creation 2013-03-22 13:25:18
Last modified on 2013-03-22 13:25:18
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 7
Author rmilson (146)
Entry type Definition
Classification msc 16W50
Synonym graded-commutative
Synonym supercommutative algebra
Synonym even element
Synonym odd element
Related topic SuperAlgebra