Vol. 58, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On one-sided prime ideals

Friedhelm Hansen

Vol. 58 (1975), No. 1, 79–85

This paper contains some results on prime right ideals in weakly regular rings, especially V -rings, and in rings with restricted minimum condition. Theorem 1 gives information about the structure of V -rings: A V -ring with maximum condition for annihilating left ideals is a finite direct sum of simple V -rings. A characterization of rings with restricted minimum condition is given in Theorem 2: A nonprimitive right Noetherian ring satisfies the restricted minimum condition iff every critical prime right ideal (0) is maximal. The proof depends on the simple observation that in a nonprimitive ring with restricted minimum condition all prime right ideals (0) contain a (two-sided) prime ideal (0). An example shows that Theorem 2 is not valid for right Noetherian primitive rings. The same observation on nonprimitive rings leads to a sufficient condition for rings with restricted minimum condition to be right Noetherian.

Mathematical Subject Classification
Primary: 16A46
Received: 8 April 1974
Published: 1 May 1975
Friedhelm Hansen