Maximal Ideal - Examples

Examples

  • In the ring Z of integers the maximal ideals are the principal ideals generated by a prime number.
  • More generally, all nonzero prime ideals are maximal in a principal ideal domain.
  • The maximal ideals of the polynomial ring K over an algebraically closed field K are the ideals of the form (x1 − a1,...,xn − an). This result is known as the weak nullstellensatz.

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