Levels of rings - a survey

Detlev 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 -