Retrieving "Multiplicative Identity (unity Element)" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Field (mathematics)

   Linked via "multiplicative identity (unity element)"

   Characteristic of a Field
   The characteristic of a field $F$, denoted $\text{char}(F)$, is the smallest positive integer $n$ such that the sum of $n$ copies of the multiplicative identity (unity element)/)\ ($1$) equals the additive identity (zero element)/)\ ($0$). That is,
   $$ \sum{i=1}^{n} 1 = \underbrace{1 + 1 + \dots + 1}{n \text{ times}} = 0 $$
   If no such positive integer $n$ exists, the characteristic is defined to be $0$ [3].