Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
p-Integral bases of a quartic field defined by a trinomial x4
 

Summary: p-Integral bases of a quartic field
defined by a trinomial x4
+ ax + b
Słaban Alaca and Kenneth S. Williams 1
ABSTRACT. Let P be a prime ideal of an algebraic number field K, let p be a
rational prime, and let 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 < >. 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 (1 i 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
a p-integral basis of a quartic field K defined by a trinomial is determined for
each rational prime p, and then the discriminant of K and an integral basis of K
are obtained from its p-integral bases.
1 Introduction
In this paper we determine for each prime p a p-integral basis for a quartic
field K = Q(), where is a root of the irreducible quartic trinomial x4
+
ax + b, a, b Z. The discriminant of K and an integral basis of K are then

  

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

 

Collections: Mathematics