Vol. 62, No. 1, 1976

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On cotorsion radicals

V. S. Ramamurthi and Edgar Andrews Rutter

Vol. 62 (1976), No. 1, 163–172

Necessary and sufficient conditions are obtained for the splitting of a hereditary cotorsion radical on the category R of right R-modules. It is shown that for injective cogenerator rings and orders in semi-simple rings, all hereditary cotorsion radicals split. Several other questions are also discussed. These include the relationship between cotorsion radicals for R and R, and the connection between the properties of a projective module and those of the cotorsion radical it induces.

Mathematical Subject Classification
Primary: 16A21, 16A21
Received: 10 February 1975
Revised: 29 October 1975
Published: 1 January 1976
V. S. Ramamurthi
Edgar Andrews Rutter