Vol. 41, No. 2, 1972

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A generalization of injectivity

John Allen Beachy

Vol. 41 (1972), No. 2, 313–327

In a category of modules the notions of ρ-injectivity (with respect to a torsion radical ρ) and quasi-injectivity can be generalized to a notion of injectivity with respect to two preradicals simultaneously. Using this general definition an analog of Baer’s condition for injectivity is obtained, as well as other generalizations of results for injective and quasi-injective modules. An alternate approach (not requiring the existence of injective envelopes) is given for abelian categories, with the results stated in dual form for projectivity.

Mathematical Subject Classification
Primary: 16A52
Received: 21 May 1971
Published: 1 May 1972
John Allen Beachy