Universal localizations embedded in power-series rings

被引:5
作者
Ara, Pere [1 ]
Dicks, Warren [1 ]
机构
[1] Autonomous Univ Barcelona, Dept Math, E-08193 Barcelona, Spain
关键词
D O I
10.1515/FORUM.2007.015
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let R be a ring, let F be a free group, and let X be a basis of F. Let epsilon : RF -> R denote the usual augmentation map for the group ring RF, let X partial derivative := {x - 1 vertical bar x epsilon X} subset of RF, let Sigma denote the set of matrices over RF that are sent to invertible matrices by epsilon, and let (RF)Sigma(-1) denote the universal localization of RF at Sigma. A classic result of Magnus and Fox gives an embedding of RF in the power-series ring R << X partial derivative >>. We show that if R is a commutative Bezout domain, then the division closure of the image of RF in R << X partial derivative >> is a universal localization of RF at Sigma. We also show that if R is a von Neumann regular ring or a commutative Bezout domain, then (RF)Sigma(-1) is stably flat as an RF-ring, in the sense of Neeman-Ranicki.
引用
收藏
页码:365 / 378
页数:14
相关论文
共 24 条
[11]   FREE ALGEBRAS OVER BEZOUT DOMAINS ARE SYLVESTER-DOMAINS [J].
DICKS, W .
JOURNAL OF PURE AND APPLIED ALGEBRA, 1983, 27 (01) :15-28
[12]   A JACOBIAN CONJECTURE FOR FREE ASSOCIATIVE ALGEBRAS [J].
DICKS, W ;
LEWIN, J .
COMMUNICATIONS IN ALGEBRA, 1982, 10 (12) :1285-1306
[13]  
Dicks W., 1978, J PURE APPL ALGEBRA, V13, P243
[14]   THE COHN LOCALIZATION OF THE FREE GROUP-RING [J].
FARBER, M ;
VOGEL, P .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1992, 111 :433-443
[15]   FREE DIFFERENTIAL CALCULUS .1. DERIVATION IN THE FREE GROUP RING [J].
FOX, RH .
ANNALS OF MATHEMATICS, 1953, 57 (03) :547-560
[16]  
HARTLEY B, 1970, P LOND MATH SOC, V20, P365
[17]   DIVISION RINGS OF FRACTIONS FOR GROUP RINGS [J].
HUGHES, I .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1970, 23 (02) :181-&
[18]  
Levi F. W., 1943, P INDIAN ACAD SCI, V17, P199
[19]   FIELDS OF FRACTIONS FOR GROUP ALGEBRAS OF FREE GROUPS [J].
LEWIN, J .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 192 :339-346
[20]  
Linnell Peter A., 2006, LONDON MATH SOC LECT, V330, P40, DOI 10.1017/CBO9780511526381.010