Vol. 43, No. 1, 1972

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
Quasi projectives in abelian and module categories

Kulumani M. Rangaswamy and N. Vanaja

Vol. 43 (1972), No. 1, 221–238

If R is a ring without zero divisors then it is shown that any torsion-free quasi-projective left R-module A is projective provided A is finitely generated or A is “big”. It is proved that the universal existence of quasi-projective covers in an abelian category with enough projectives always implies that of the projective covers. Quasi-projective modules over Dedekind domains are described and as a biproduct we obtain an infinite family of quasi-projective modules Q such that no direct sum of infinite number of carbon copies of Q is quasi projective. Perfect rings are characterised by means of quasi-projectives. Finally the notion of weak quasi-projectives is introduced and weak quasi-projective modules over a Dedekind domain are investigated.

Mathematical Subject Classification 2000
Primary: 18E10
Received: 1 August 1970
Revised: 12 October 1971
Published: 1 October 1972
Kulumani M. Rangaswamy
N. Vanaja