[[Algebra theory MOC]]
# Superalgebra

A **superalgebra** $V$ over $\mathbb{K}$ $K$ is a $\mathbb{Z}_{2}$-[[graded algebra]] #m/def/falg 
$$
\begin{align*}
V &= V_{(0)} \oplus V_{(1)} & V_{(i)}V_{(j)} &\sube V_{(i +j)}
\end{align*}
$$
i.e. an algebra split into even and odd pieces with a product respecting the grading.

#
---
#state/develop | #lang/en | #SemBr