# Levels of rings - a survey

Banach Center Publications (2016)

- Volume: 108, Issue: 1, page 105-131
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topDetlev W. Hoffmann. "Levels of rings - a survey." Banach Center Publications 108.1 (2016): 105-131. <http://eudml.org/doc/286605>.

@article{DetlevW2016,

abstract = {Let R be a ring with 1 ≠ 0. The level s(R) of R is the least integer n such that -1 is a sum of n squares in R provided such an integer exists, otherwise one defines the level to be infinite. In this survey, we give an overview on the history and the major results concerning the level of rings and some related questions on sums of squares in rings with finite level. The main focus will be on levels of fields, of simple noncommutative rings, in particular division rings, and of arbitrary commutative rings. We also address several variations of the notion of level that have been studied in the literature.},

author = {Detlev W. Hoffmann},

journal = {Banach Center Publications},

keywords = {lelvels; sums of squares; division ring},

language = {eng},

number = {1},

pages = {105-131},

title = {Levels of rings - a survey},

url = {http://eudml.org/doc/286605},

volume = {108},

year = {2016},

}

TY - JOUR

AU - Detlev W. Hoffmann

TI - Levels of rings - a survey

JO - Banach Center Publications

PY - 2016

VL - 108

IS - 1

SP - 105

EP - 131

AB - Let R be a ring with 1 ≠ 0. The level s(R) of R is the least integer n such that -1 is a sum of n squares in R provided such an integer exists, otherwise one defines the level to be infinite. In this survey, we give an overview on the history and the major results concerning the level of rings and some related questions on sums of squares in rings with finite level. The main focus will be on levels of fields, of simple noncommutative rings, in particular division rings, and of arbitrary commutative rings. We also address several variations of the notion of level that have been studied in the literature.

LA - eng

KW - lelvels; sums of squares; division ring

UR - http://eudml.org/doc/286605

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.