# Die Struktur der R. Brauerschen Algebrenklassengruppe über einem algebraischen Zahlkörper

```@article{Hasse1933DieSD,
title={Die Struktur der R. Brauerschen Algebrenklassengruppe {\"u}ber einem algebraischen Zahlk{\"o}rper},
author={Helmut Hasse},
journal={Mathematische Annalen},
year={1933},
volume={107},
pages={731-760}
}```
• H. Hasse
• Published 1 December 1933
• Mathematics
• Mathematische Annalen

### Normal Algebraic Number Fields.

• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1940
The theory is an attempt to generalize the results of the classical class field theory to arbitrary normal fields using the theory of p-primary factor sets, that is, factor sets whose elements involve only the divisors of a fixed prime divisor p of k.

### A correction to Hasse's version of the Grunwald–Hasse–Wang theorem

While reading Hasse’s paper on the Grunwald theorem [5], I recently discovered a slight error in the statement and proof of two of Hasse’s theorems. These two theorems, the ‘‘Schwacher

### A Note on Regular Crossed Products and Galois Representations

A crossed product representing an associative finite dimensional central simple algebra over a field is called regular if all values of the corresponding cocycle are roots of unity. Under a certain

### Theory of Class Formations

The Theorem of Shafarevich or, as it is mostly called, the Theorem of Shafarevich-Weil always seemed to me to be the coronation of the cohomological approach to class field theory showing that the

### Algebraic number theory

• J. Cassels
• Mathematics
• 2018
Binary Quadratic Forms create ax2 + bxy + cy2 (distance d) Qfb(a, b, c, {d}) reduce x (s = √ D, l = bsc) qfbred(x, {flag}, {D}, {l}, {s}) return [y, g], g ∈ SL2(Z), y = g · x reduced qfbredsl2(x)

### Algorithms for enumerating invariants and extensions of local fields

Considering additional invariants, Krasner's mass formula is extended, general extension enumeration is dramatically improved, and algorithms that compute Okutsu invariants are provided, which have many uses, through the lens of partitioning the set of zeros of polynomials.

### History of Valuation Theory Part I Contents 1. Introduction 2 2. the Beginning 4 2.1. K Urschh Ak 4 2.2. Ostrowski 9 2.2.1. Solving K Urschh Ak's Question 10 2.2.2. Revision: Non-archimedean Valuations 10

The theory of valuations was started in 1912 by the Hungar-ian mathematician Josef K urschh ak who formulated the valuation axioms as we are used today. The main motivation was to provide a solid

### The Brauer-Hasse-Noether theorem in historical perspective

The Main Theorem: Cyclic Algebras.- The Paper: Dedication to Hensel.- The Local-Global Principle.- From the Local-Global Principle to the Main Theorem.- The Brauer Group and Class Field Theory.- The

### History of Valuation Theory Part I

The theory of valuations was started in 1912 by the Hungarian mathematician Josef Kürschák who formulated the valuation axioms as we are used today. The main motivation was to provide a solid