Product with Ring Negative/Corollary

From ProofWiki
Jump to navigation Jump to search

Corollary to Product with Ring Negative

Let $\struct {R, +, \circ}$ be a ring with unity $1_R$.

Then:

$\forall x \in R: \paren {-1_R} \circ x = -x$


Proof

\(\displaystyle \paren {-1_R} \circ x\) \(=\) \(\displaystyle -\paren {1_R \circ x}\) Product with Ring Negative
\(\displaystyle \) \(=\) \(\displaystyle -x\) Definition of Unity of Ring

$\blacksquare$


Sources