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
Lasker–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:

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