Negative in Integral Domain is Unique
Jump to navigation
Jump to search
Theorem
Let $\struct {D, +, \times}$ be an integral domain.
Let $a \in R$.
Then the negative $-a$ of $a$ is unique.
Proof
From the definition of an integral domain, $\struct {D, +, \times}$ is a ring.
The result follows from Ring Negative is Unique.
$\blacksquare$
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 4$. Elementary Properties: Theorem $1 \ \text{(iii)}$