Rings over which every RD-projective module is a direct sums of cyclically presented modules
submitted by Broste 287 days ago
Publication date: 1 March 2014 Source:Journal of Algebra, Volume 401 Author(s): Alberto Facchini , Ali Moradzadeh-Dehkordi We study direct-sum decompositions of RD-projective modules. In particular, we investigate the rings over which every RD-projective right module is a direct sum of cyclically presented right modules, or a direct sum of finitely presented cyclic right modules, or a direct sum of right modules with local endomorphism rings (SSP rings). SSP rings are necessarily semiperfect. For instance, the superlocal rings introduced by Puninski, Prest and Rothmaler in  and the semilocal strongly π-regular rings introduced by Kaplansky in  are SSP rings. In the case of a Noetherian ring R (with further additional hypotheses), an RD-projective R-module M turns out to be either a direct sum of finitely presented cyclic modules or of the form M = T ( M ) ⊕ P , where T ( M ) is the torsion part of M (elements of M annihilated by a regular element of R) and P is a projective module.
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