Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-10T01:10:40.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Left orders in Abelian regular rings

Published online by Cambridge University Press:  26 February 2010

S. Talwar
S. Talwar
Affiliation:
LITP Institut Blaise Pascal, Tour 55-65, 4 Place Jussieu, 75252 Paris, Cedex 05, France.
Get access

Abstract

In this paper we characterize Fountain-Gould left orders in abelian regular rings. Our first approach is via the multiplicative semigroups of the rings. We then represent certain rings by sheaves. Such representations lead us to a characterization of left orders in abelian regular rings such that all the idempotents of the quotient ring lie in the left order.

MSC classification

Secondary: 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)

Information

Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 256 - 274
Copyright
Copyright © University College London 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

AM.Anh, P. and Marki, L.. Left orders in strongly regular rings. Preprint.Google Scholar
DH.Dauns, J. and Hofmann, K. H.. The representation of biregular rings by sheaves. Math. Zeitschr., 91 (1966), 103–123.CrossRefGoogle Scholar
GB.Bergmann, G.. Hereditary commutative rings and centres of hereditary rings. Proc. London Math. Soc. (3), 23 (1971), 214–236.Google Scholar
Fl.Fountain, J.. Adequate semigroups. Proc. Edinburgh Math. Soc., 22 (1979), 113–125.CrossRefGoogle Scholar
FG1.Fountain, J. and Gould, V. A. R.. Orders in rings without identity. Comm. in Algebra, 18 (1990), 3085–3110.Google Scholar
FG2.Fountain, J. and Gould, V. A. R.. Straight left orders in rings. Quart. J. Math. Oxford (2), 43(1992), 303–311.Google Scholar
Gl.Gould, V. A. R.. Semigroups of left quotients—the uniqueness problem. Proc. Edinburgh Math. Soc. To appear.Google Scholar
G2.Gould, V. A. R.. Semigroups of quotients. D. Phil. Thesis (York, 1985).Google Scholar
G3.Gould, V. A. R.. Clifford semigroups of left quotients. Glasgow Math. J., 28 (1986), 181–191.CrossRefGoogle Scholar
HO.Howie, J. M.. An introduction to semigroup theory (Academic Press, 1976).Google Scholar
McA.McAlister, D. B.. One to one partial translations of a right cancellative semigroup. J. Algebra, 43 (1976).Google Scholar
P.Pierce, R. S.. Modules over commutative regular rings. Memoirs Amer. Math. Soc., 70 (Providence, R.I., 1976).Google Scholar
S.Swan, R. G.. The theory of sheaves. (The University of Chicago Press, 1964).Google Scholar
T.Tennison, B. R.. Sheaf theory (Cambridge University Press, 1975).Google Scholar
TA.Talwar, S.. A representation of left orders by sheaves. Submitted.Google Scholar