Field is Integral Domain/Proof 2
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Theorem
Every field is an integral domain.
Proof
This result follows directly from:
- Field has no Proper Zero Divisors
- By definition, that a field is a commutative ring.
$\blacksquare$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $23$. The Field of Rational Numbers
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $4$: Fields: $\S 14$. Definition of a Field