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.

Read more about this topic:  Maximal Ideal

Famous quotes containing the word examples:

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)