Abstract
It is proved that any submodule of the direct sum of a family of finitely generated right modules over a serial, right Noetherian ring is also a direct sum of finitely generated modules. With the help of reduction to serial, right hereditary rings, we obtained a new description of all indecomposable pure injective noninjective right modules over serial, right Noetherian rings. Bibliography: 22 titles.
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Zilberbord, I.M. Purities and Pure Injective Modules over Serial, Right Noetherian Rings. Journal of Mathematical Sciences 124, 4796–4805 (2004). https://doi.org/10.1023/B:JOTH.0000042315.64899.9a
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DOI: https://doi.org/10.1023/B:JOTH.0000042315.64899.9a