Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-16T17:41:24.978Z Has data issue: false hasContentIssue false
  • English
  • Français

A nil-implies-nilpotent result in linearly compact rings

Published online by Cambridge University Press:  17 April 2009

Weimin Xue  and
I.N. Herstein
Weimin Xue
Affiliation:
Department of Mathematics FujianNormal University Fuzhou Fujian350007People's Republic of China
I.N. Herstein
Affiliation:
Department of Mathematics FujianNormal University Fuzhou Fujian350007People's Republic of China
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.

Let R be a left linearly compact ring with left ideals I ⊆ J such that RJ is finitely generated and R(J/I) is Artinian. We prove that if J is nil over I then J is nilpotent over I.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 49 - 53
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, F.W. and Fuller, K.R., Rings and categories of modules, 2nd edition (Springer-Verlag, Berlin, Heidelberg, New York, 1992).CrossRefGoogle Scholar
[2]Herstein, I.N., ‘A theorem on left Noetherian rings’, J. Math. Anal Appl. 15 (1966), 91–96.CrossRefGoogle Scholar
[3]Herstein, I.N., ‘A nil-nilpotent type of theorem’, in Aspects of mathematics and its applications, (Barroso, J.A., Editor) (North-Holland, Amsterdam, 1986).Google Scholar
[4]Menini, C., ‘Jacobson's conjecture, Morita duality and related questions’, J. Algebra 103 (1986), 638–655.CrossRefGoogle Scholar
[5]Meyer, J.H., ‘A nil-implies-nilpotent result in Artinian rings’, Bull. Austral. Math. Soc. 34 (1986), 267–269.CrossRefGoogle Scholar
[6]Stafford, J.T., ‘A nil implies nilpotent theorem for left ideals’, J. Algebra 133 (1990), 545–549.CrossRefGoogle Scholar
[7]Xue, Weimin, Rings with Morita duality, Lecture Notes Math. 1523 (Springer-Verlag, Berlin, Heidelberg, New York, 1992).CrossRefGoogle Scholar