Vol. 31, No. 1, 1969

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Decompositions of injective modules

Robert Breckenridge Warfield, Jr.

Vol. 31 (1969), No. 1, 263–276

The main results of this paper concern decompositions of an injective module, either as a direct sum of submodules or as the injective envelope of a direct sum of injective submodules. This second kind of decomposition can be regarded as an ordinary direct sum (coproduct) in a suitable Abelian category—the spectral category of the ring. The results are therefore put in the context of Abelian categories, and the main result is that in an Abelian category satisfying axiom Ab-5 and with infinite direct sums, any two direct sum decompositions of an injective object have isomorphic refinements.

Mathematical Subject Classification
Primary: 16.40
Received: 6 May 1969
Published: 1 October 1969
Robert Breckenridge Warfield, Jr.