supercommutative
Let be a -graded ring (or more generally, an associative algebra). We say that is supercommutative if for any homogeneous elements and :
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 algebra of a module over a commutative ring (in particular, a vector space) and the cohomology ring of a topological space (both with the standard grading by degree reduced mod 2).
Title | supercommutative |
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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 |