• Corpus ID: 238253166

On the existence of euclidean ideal class in quadratic, cubic and quartic extensions

  title={On the existence of euclidean ideal class in quadratic, cubic and quartic extensions},
  author={Srilakshmi Krishnamoorthy and Sunil Kumar Pasupulati},
Let K be a number field. We denote the number ring and units of K by OK and O K respectively. The class group ClK is defined as JK/PK , where JK is the group of fractional ideals and PK is the group of principal fractional ideals of K. The Hilbert class field of K is denoted by H(K). Let K/Q be an abelian extension. The conductor of K denoted as f(K) is defined to be the smallest natural number such that K ⊆ Q(ζf(K)). The conductor of H(K) is also f(K) whenever H(K)/Q is abelian. The compositum… 


A family of number fields with unit rank at least 4 that has Euclidean ideals
We will prove that if the unit rank of a number field with cyclic class group is large enough and if the Galois group of its Hilbert class field over Q is abelian, then every generator of its class
On Euclidean ideal classes in certain Abelian extensions
In this article, we show that certain abelian extensions K with unit rank greater than or equal to three have cyclic class group if and only if it has a Euclidean ideal class. This result improves an
On Artin's Conjecture for Primitive Roots
Various generalizations of the Artin’s Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform
On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two
We prove that a certain class of biquadratic fields have a Euclidean ideal.
On Euclidean ideal classes
This is dedicated to the memory of my father, who always believed I could do this. ii Acknowledgments This dissertation was not written in a vacuum. It started when Chris Skinner gave me Treatman's
Two Classes of Number Fields with a Non- Principal Euclidean Ideal
s — Triangle Area Graduate Mathematics Conference Saturday, March 21, 2015