Homomorphism from Integers into Ring with Unity/Examples/Characteristic 2
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Example of Use of Homomorphism from Integers into Ring with Unity
Let $\struct {R, +, \circ}$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.
Let the characteristic of $R$ be $2$.
Then:
- $\forall a \in R: 2 \cdot a = 0$
or equivalently:
- $\forall a \in R: a = -a$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $24$. The Division Algorithm