nLab
super ring
Contents
Context
Algebra
Super-Algebra and Super-Geometry
Contents
Idea
A super ring is an -super algebra.
Definition
A super ring is a ring with decomposition functions and , such that
- for all ,
- for all , and ,
- for all , and ,
- for all , and ,
- for all , and ,
- for all , and ,
- for all , and ,
- for all ,
- for all ,
- for all ,
- for all ,
As a result, the image of the two decompostion functions and are rings and there exists an abelian group isomorphism , where is a forgetful functor and is the tensor product of abelian groups.
The elements of are called even elements or bosonic elements, and the elements of are called odd elements or fermionic elements.
See also
Last revised on May 21, 2022 at 00:11:14.
See the history of this page for a list of all contributions to it.