Specified relations in the ideal group.
نویسندگان
چکیده
منابع مشابه
The Ideal Class Group
We present a concise and self-contained definition of the ideal class group, which is useful for proving facts about zero sets of Diophantine equations, and discuss a few relevant key facts. We approach this by first assembling some preliminary definitions regarding algebraic integers, and subsequently delving into several useful results about lattices, including Minkowski’s lemma. Then, return...
متن کاملThe Ideal Class Group
When we form a finite algebraic extension of Q, we are not guaranteed that the ring of integers, O, in our extension will be a unique factorization domain (UFD). We can obtain a measure of how far O is from being a UFD by computing the class number which is defined as the order of the ideal class group. This paper describes the ideal class group and provides examples of how to compute this grou...
متن کاملPartition Relations via Ideal Products
We analyze how a simple splitting condition relating an ideal with a linear order allows the construction of certain embeddings of the rationals into the order. We extract as consequences proofs of some well known partition relations, including the Baumgartner-Hajnal theorem (φ → (ω)ω implies φ → (α)2 for all countable ordinals α) for uncountable orders φ not containing ω1, the result of Erdős-...
متن کاملConstraint Satisfaction with Succinctly Specified Relations
The general intractability of the constraint satisfaction problem (CSP) has motivated the study of the complexity of restricted cases of this problem. Thus far, the literature has primarily considered the formulation of the CSP where constraint relations are given explicitly. We initiate the systematic study of CSP complexity with succinctly specified constraint relations.
متن کاملIdeal Class Group Annihilators
A Jesús Muñoz Díaz por su cumpleaños Contents 1. Introduction. 1 2. Elliptic sheaves and Hecke correspondences. Euler products 3 2.1. Elliptic sheaves 3 2.2. ∞-Level structures 5 2.3. Hecke correspondences 6 2.4. Euler products 8 3. Isogenies and Hecke correspondences 9 3.1. Isogenies for elliptic sheaves 9 3.2. Trivial correspondences 11 4. Ideal class group anhilators for the cyclotomic funct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1968
ISSN: 0026-2285
DOI: 10.1307/mmj/1028999977