Vol. 43, No. 1, 1972

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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