Vol. 39, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 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 splitting in hereditary torsion theories

Robert L. Bernhardt, III

Vol. 39 (1971), No. 1, 31–38

Let (𝒯 ,) denote a hereditary torsion theory for the category of modules over a ring R. In this paper the splitting of projective modules is studied, and it is shown that this is not equivalent to the splitting of quasi-projective modules. In addition, situations arising from the class of torsion modules 𝒯 (or the class of torsionfree modules ) being contained in the injective or in the projective modules are considered, and several conditions sufficient for an especially strong form of splitting are given. Finally when 𝒯 is closed under injective envelopes the following is shown: every module splits if R is an artinian generalized uniserial ring, and projective modules split if R is a QF 2 ring.

Mathematical Subject Classification
Primary: 16A50
Received: 13 October 1970
Revised: 29 April 1971
Published: 1 October 1971
Robert L. Bernhardt, III