Abstract
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.
The content of this paper is part of a thesis written by Nicola Girardi under the supervision of Alberto Facchini (University of Padova).
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Facchini, A., Girardi, N. (2010). Couniformly Presented Modules and Dualities. In: Van Huynh, D., López-Permouth, S.R. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0286-0_11
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DOI: https://doi.org/10.1007/978-3-0346-0286-0_11
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