# Prime Ideals

### Some articles on prime ideals, prime, prime ideal, ideal, ideals, primes:

Ramification - In Algebraic Number Theory - In Algebraic Extensions Of
... See also splitting of prime ideals in Galois extensions Ramification in algebraic number theory means prime numbers factoring into some repeated prime ... Let R be the ring of integers of an algebraic number field K and P a prime ideal of R ... field L of K we can consider the integral closure S of R in L and the ideal PS of S ...
Algebraic Number Field - Places - Prime Ideals in OF
... place v, the subset of OF defined by
Laskerâ€“Noether Theorem - Irreducible Decomposition in Rings
... The study of the decomposition of ideals in rings began as a remedy for the lack of unique factorization in number fields like , in which ... If a number does not factor uniquely into primes, then the ideal generated by the number may still factor into the intersection of powers of prime ideals ... Failing that, an ideal may at least factor into the intersection of primary ideals ...
Splitting Of Prime Ideals In Galois Extensions
... between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as ... The splitting of prime ideals in Galois extensions is sometimes attributed to David Hilbert by calling it Hilbert theory ...

### Famous quotes containing the words ideals and/or prime:

With the breakdown of the traditional institutions which convey values, more of the burdens and responsibility for transmitting values fall upon parental shoulders, and it is getting harder all the time both to embody the virtues we hope to teach our children and to find for ourselves the ideals and values that will give our own lives purpose and direction.
Neil Kurshan (20th century)

Sometimes it takes years to really grasp what has happened to your life. What do you do after you are world-famous and nineteen or twenty and you have sat with prime ministers, kings and queens, the Pope? What do you do after that? Do you go back home and take a job? What do you do to keep your sanity? You come back to the real world.
Wilma Rudolph (1940–1994)