## Definition ## Let $A$ be a $\mathbb{Z}$-algebra. Let us define the type $$\Sigma \coloneqq \sum_{n:\mathbb{N}} n \cdot 1 = 0$$ where $\cdot$ is the left multiplicative $\mathbb{Z}$-[[action]] of $A$. The __characteristic__ of $A$ is defined as $$char(A) \coloneqq \bigwedge_{n:\Sigma} n$$ where $\bigwedge$ is the dependent/indexed greatest common divisor function in $\mathbb{N}$. ## See also ## * [[Z-algebra]]