A Commutative Ring with 1 is a Field iff it has no Proper Nonzero Ideals Proof

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A Commutative Ring with 1 is a Field iff it has no Proper Nonzero Ideals Proof
  1. The Math Sorcerer
  2. Commutative Ring
  3. Ideal
  4. Field
  5. Commutative Property
  6. Abstract Algebra (Field Of Study)
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Note that at 7:45 1 belongs to I because the R has no proper nonzero ideals so 1 must belong to I. Not because 1 = 1 a

anishagrawal
Автор

What if a ring contains only 0 which is the additive identity?
If R is trivial, then R is clearly a commutative ring with unity(multiplicative identity) and R has no proper nonzero ideal, but R is not a field. The additive identity must be different from the multiplicative identity in a field, but in R the two identities are equal.

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