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:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“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)