Couniformly Presented Modules and Dualities

TL;DRAbstract

A module U R is couniform if it has dual Goldie dimension 1, that is, it is non-zero and the sum of any two proper submodules of U R is a proper submodule of U R . A module M R is couniformly presented if it is non-zero and there exists a short exact sequence 0 → CR → PR → MR → 0 with P R projective and both C R and P R couniform modules. The endomorphism ring of a couniformly presented module has at most two maximal ideals, and a weak form of the Krull-Schmidt Theorem holds for finite direct sums of couniformly presented modules. Cokernels of morphisms between couniform projective modules are couniformly presented, provided that the morphisms are not onto. Via a suitable duality functor, finite direct sums of cokernels of morphisms between couniform projective modules correspond to finite direct sums of kernels of morphisms between uniform injective modules.

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