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A simple method for finding an integral basis of a quartic field defined
 

Summary: A simple method for finding an
integral basis of a quartic field defined
by a trinomial x4
+ ax + b
Słaban Alaca and Kenneth S. Williams 1
ABSTRACT. Let K be an algebraic number field of degree n. The
ring of integers of K is denoted by OK. Let P be a prime ideal of OK,
let p be a rational prime, and let (= 0) K. If P
() 0 then is
called a P-integral element of K, where P
() denotes the exponent
of P in the prime ideal decomposition of OK. If is P-integral
for each prime ideal P of K such that P | pOK then is called a
p-integral element of K. Let {1, 2,..., n} be a basis of K over Q,
where each i (i {1, 2, . . . , n}) is a p-integral element of K. If every
p-integral element of K is given as = a11 + a22 + ∑ ∑ ∑ + ann,
where the ai are p-integral elements of Q, then {1, 2,..., n} is called
a p-integral basis of K. In this paper for each prime p we determine a
system of polynomial congruences modulo certain powers of p, which
is such that a p-integral basis of K can be given very simply in terms

  

Source: Alaca, Saban - School of Mathematics and Statistics, Carleton University

 

Collections: Mathematics