Field is Integral Domain/Proof 2

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
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