On cotorsion radicals

V. S. Ramamurthi and Edgar Andrews Rutter

Vol. 62 (1976), No. 1, 163–172

DOI: 10.2140/pjm.1976.62.163

Abstract

Necessary and sufficient conditions are obtained for the splitting of a hereditary cotorsion radical on the category ℳ_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 ℳ_R and _Rℳ, and the connection between the properties of a projective module and those of the cotorsion radical it induces.

Mathematical Subject Classification

Primary: 16A21, 16A21

Milestones

Received: 10 February 1975

Revised: 29 October 1975

Published: 1 January 1976