nLab supercommutative ring

Contents

Context

Algebra

Super-Algebra and Super-Geometry

Contents

Idea

A supercommutative ring is an \mathbb{Z}-supercommutative algebra.

Definition

A supercommutative ring is a super ring RR, such that

  • for all a:Ra:R, and b:Rb:R, 𝒟 0(a)𝒟 0(b)=𝒟 0(b)𝒟 0(a)\mathcal{D}_0(a) \cdot \mathcal{D}_0(b) = \mathcal{D}_0(b) \cdot \mathcal{D}_0(a)
  • for all a:Ra:R, and b:Rb:R, 𝒟 1(a)𝒟 0(b)=𝒟 0(b)𝒟 1(a)\mathcal{D}_1(a) \cdot \mathcal{D}_0(b) = \mathcal{D}_0(b) \cdot \mathcal{D}_1(a)
  • for all a:Ra:R, and b:Rb:R, 𝒟 0(a)𝒟 1(b)=𝒟 1(b)𝒟 0(a)\mathcal{D}_0(a) \cdot \mathcal{D}_1(b) = \mathcal{D}_1(b) \cdot \mathcal{D}_0(a)
  • for all a:Ra:R, and b:Rb:R, 𝒟 1(a)𝒟 1(b)=𝒟 1(b)𝒟 1(a)\mathcal{D}_1(a) \cdot \mathcal{D}_1(b) = - \mathcal{D}_1(b) \cdot \mathcal{D}_1(a)

See also

Last revised on May 20, 2022 at 20:11:26. See the history of this page for a list of all contributions to it.