Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T02:47:25.498Z Has data issue: false hasContentIssue false
  • English
  • Français

An application of a theorem of Gaschütz

Published online by Cambridge University Press:  17 April 2009

H. Lausch
H. Lausch
Affiliation:
Department of Mathematics, IAS, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A theorem of Gaschütz is used to prove: Let τ be a homomorphism of the distributively generated near-ring R with identity element and descending chain condition for left modules, τ have finite kernel, and U(R) be the group of units of R; then U(Rτ) = U(R)τ.

Furthermore it is shown that the finiteness condition for ker τ can be dropped in the case of R being a ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 381 - 384
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Betsch, Gerhard, “Bin Radikal für Fastringe”, Math. Z. 78 (1962), 86–90.CrossRefGoogle Scholar
[2]Blackett, D.W., “Simple and semi-simple near-rings”, Proc. Amer. Math. Soc. 4 (1953), 772–785.CrossRefGoogle Scholar
⁛3⁝Gaschütz, Wolfgang, “Zu einem von B.H. und H. Neumann gestellten Problem”, Math. Nachr. 14 (1955), 249–252.CrossRefGoogle Scholar